The generator matrix
1 0 1 1 1 0 1 1 0 1 1 0 X 1 1 1 1 0 1 X 1 1 1 0 1 1 0 1 X 1 1 1 1 0 1 X 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 X 0 1 1 0 0 1 1 0 X 1
0 1 1 0 1 1 0 1 1 X X+1 1 1 0 X+1 0 X+1 1 X+1 1 X 0 X+1 1 X+1 0 1 0 1 X+1 0 X+1 X+1 1 0 1 X X 1 X 1 0 0 X X+1 X+1 X 0 1 X 1 1 X+1 1 1 1 X 1 1 X X+1 1 1 0
0 0 X 0 0 0 0 0 0 0 X 0 0 X X X X 0 0 0 0 X X X X 0 0 X X X 0 X 0 0 X X 0 0 X 0 0 X X 0 X 0 X 0 X X 0 0 0 X X X 0 0 X 0 X 0 X X
0 0 0 X 0 0 0 0 0 X 0 0 0 0 X X 0 X X X X X X X X 0 X X 0 0 0 X X X X X X X X 0 X 0 0 0 0 X X 0 X 0 0 0 X X X 0 0 X X 0 0 X X X
0 0 0 0 X 0 0 0 0 0 X X X X 0 X X X X X 0 X X X 0 X 0 X X 0 X X X 0 X 0 X X X 0 0 X 0 X 0 X 0 X 0 X 0 X 0 X 0 0 X 0 X X X X 0 X
0 0 0 0 0 X 0 0 X 0 0 X 0 X 0 X 0 X 0 0 0 X X X X 0 X 0 X X 0 0 X 0 0 0 X 0 X X 0 0 0 X X X X X X 0 0 0 X 0 0 X X X 0 0 X 0 0 0
0 0 0 0 0 0 X 0 X X 0 0 X X 0 0 X 0 X 0 X X X X 0 0 0 0 X X X 0 0 0 X 0 X 0 0 X 0 X X 0 0 X X 0 X 0 X X X X X X X X X 0 X X 0 X
0 0 0 0 0 0 0 X X 0 X 0 X X X 0 0 X 0 X X X 0 X X X 0 0 X X X X 0 0 X X X X X X X 0 0 X 0 0 0 0 X X 0 0 0 0 0 0 0 X X 0 0 0 0 X
generates a code of length 64 over Z2[X]/(X^2) who´s minimum homogenous weight is 56.
Homogenous weight enumerator: w(x)=1x^0+80x^56+128x^58+146x^60+128x^62+92x^64+128x^66+113x^68+128x^70+54x^72+12x^76+9x^80+1x^84+4x^88
The gray image is a linear code over GF(2) with n=128, k=10 and d=56.
This code was found by Heurico 1.16 in 0.211 seconds.