Best double circulant found so far for 38

10011000001101010111001001011000111111
11001100000110101011100100101100011111
11100110000011010101110010010110001111
01110011000001101011111001001011000111
10111001100000110101111100100101100011
01011100110000011011111110010010110001
10101110011000001101111111001001011000
01010111001100000110111111100100101100
10101011100110000010011111110010010110
11010101110011000000001111111001001011
01101010111001100001000111111100100101
00110101011100110001100011111110010010
00011010101110011000110001111111001001
00001101010111001101011000111111100100
00000110101011100110101100011111110010
10000011010101110010010110001111111001
11000001101010111001001011000111111100
01100000110101011100100101100011111110
00110000011010101110010010110001111111
11111110001101001000001010100111110011
01111111000110100101000101010011111001
00111111100011010011100010101001111100
10011111110001101000110001010100111110
01001111111000110100011000101010011111
00100111111100011011001100010101001111
10010011111110001101100110001010100111
01001001111111000111110011000101010011
10100100111111100011111001100010101001
11010010011111110001111100110001010100
01101001001111111000111110011000101010
00110100100111111100011111001100010101
00011010010011111111001111100110001010
10001101001001111110100111110011000101
11000110100100111111010011111001100010
11100011010010011110101001111100110001
11110001101001001111010100111110011000
11111000110100100110101010011111001100
11111100011010010010010101001111100110

M M^T:

 20 11 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 11 20 11 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 10 11 20 11 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 10 10 11 20 11 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 10 10 10 11 20 11 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 10 10 10 10 11 20 11 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 10 10 10 10 10 11 20 11 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 10 10 10 10 10 10 11 20 11 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 10 10 10 10 10 10 10 11 20 11 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 10 10 10 10 10 10 10 10 11 20 11 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 10 10 10 10 10 10 10 10 10 11 20 11 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 10 10 10 10 10 10 10 10 10 10 11 20 11 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 10 10 10 10 10 10 10 10 10 10 10 11 20 11 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 10 10 10 10 10 10 10 10 10 10 10 10 11 20 11 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 10 10 10 10 10 10 10 10 10 10 10 10 10 11 20 11 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 20 11 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 20 11 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 20 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 11 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 20 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 21 12 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12
 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 21 12 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 21 12 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 21 12 11 11 11 11 11 11 11 11 11 11 11 11 11 11
 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 21 12 11 11 11 11 11 11 11 11 11 11 11 11 11
 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 21 12 11 11 11 11 11 11 11 11 11 11 11 11
 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 21 12 11 11 11 11 11 11 11 11 11 11 11
 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 21 12 11 11 11 11 11 11 11 11 11 11
 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 21 12 11 11 11 11 11 11 11 11 11
 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 21 12 11 11 11 11 11 11 11 11
 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 21 12 11 11 11 11 11 11 11
 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 21 12 11 11 11 11 11 11
 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 21 12 11 11 11 11 11
 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 21 12 11 11 11 11
 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 21 12 11 11 11
 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 21 12 11 11
 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 21 12 11
 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 21 12
 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 21

Determinant 21300927203883452431 (2.13009e+19) set 779 result 3.51013e+13
A = 10 B = 11 N = 19

 10  5  5  4  6  5  5  6  5  4
 11  7  6  7  5  6  6  5  6  7
 21 12 11 11 11 11 11 11 11 11