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.