The generator matrix

1 0 0 0 0 1 1 1 0 X 1 1 0 1 1 X 1 0 1 1 1 0 X X X 1 0 1 1 0 1 1 0 1 X 0 X X 1 1 1 0 1 1 0 X X X 0 1 1 X 1 1 X X 0 1 0 X 1 1 1 1
0 1 0 0 0 0 0 X 0 0 X X X 0 0 X 1 1 1 X+1 1 1 1 1 1 X+1 1 X X+1 1 X+1 1 X X 1 1 1 1 X+1 1 1 1 1 1 1 0 0 0 1 1 X 0 1 1 X 1 1 X+1 X 1 X 0 0 X
0 0 1 0 0 0 1 1 1 X 0 X+1 1 X+1 X 1 X+1 X 1 0 X+1 X+1 X+1 1 0 X 0 0 X X+1 1 X 1 0 X+1 0 X+1 1 X 0 X+1 X+1 1 X 1 X 1 1 1 X X 1 0 X X X+1 X X+1 X 1 X+1 1 0 X+1
0 0 0 1 0 1 X X+1 1 1 0 1 X 0 X+1 1 0 1 1 1 X X+1 X X+1 0 X 1 X+1 X+1 X+1 1 X X+1 X 0 X X X+1 0 1 1 X X+1 0 X X 0 0 1 1 1 X+1 0 X 0 X+1 X+1 1 1 1 X X X+1 1
0 0 0 0 1 X 0 0 X 1 X+1 X+1 1 X+1 1 X+1 1 0 1 0 X 1 0 X X+1 X+1 1 X 1 X+1 X X X X+1 X+1 0 1 0 0 X+1 0 X X+1 X+1 X+1 1 0 X 0 X 0 X+1 1 1 1 0 1 X 1 X+1 X X 0 X

generates a code of length 64 over Z2[X]/(X^2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+50x^57+90x^58+78x^59+96x^60+102x^61+68x^62+62x^63+75x^64+68x^65+40x^66+40x^67+36x^68+30x^69+38x^70+32x^71+30x^72+30x^73+18x^74+10x^75+16x^76+2x^77+2x^78+2x^79+2x^80+4x^81+2x^85

The gray image is a linear code over GF(2) with n=128, k=10 and d=57.
This code was found by Heurico 1.10 in 0.062 seconds.