The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  0  1  0  0  1  X  1  1  1  0  1  X  1  1  1  X  1  1  X  1  1  0  0  1  X  0  X  0  1  0  0  X  1  1  1  1  1  1  1  X  0  1  1  1  1  1  X  0  1  0  X
 0  1  0  0  1  1  1  0  X  1 X+1  1  1  0  X  1  1  0  X  1 X+1  X  0  X  1 X+1  X X+1  1  0  X  1  1 X+1  1  X  0  1  0  1  1  X  1  X  X  X  X  1  0  X  0 X+1  X  1  1  1  0 X+1  1  X  X  1  1  1
 0  0  1  1  1  0  1  0  1 X+1  0  X  1  1  1  X  1  X  1  0  1  1  1  X  1  X  0  0  X  X  1  1  1 X+1  X  1  X  1  1 X+1  0  0 X+1  1  1  1  0  X X+1 X+1  1  0  1  X  X  1  0 X+1  1  1  1 X+1  X X+1
 0  0  0  X  0  0  0  0  0  X  0  0  X  X  0  0  X  X  X  0  0  0  X  0  X  0  X  X  X  X  0  0  0  X  X  0  X  X  X  X  X  0  X  0  X  X  0  X  X  0  X  X  0  X  0  0  X  X  X  X  0  X  0  X
 0  0  0  0  X  0  0  0  0  0  X  X  X  0  0  X  0  0  0  X  0  X  X  X  0  X  X  X  X  X  X  0  0  X  X  0  X  X  0  0  X  X  0  0  X  0  0  X  0  X  X  0  0  X  0  0  0  0  X  0  X  0  0  0
 0  0  0  0  0  X  0  0  X  0  0  X  0  X  0  0  0  0  0  X  0  X  X  0  X  0  0  0  X  0  X  X  X  X  0  0  0  X  0  X  X  0  X  X  0  X  X  X  X  X  0  X  X  0  0  0  X  X  0  0  X  0  X  X
 0  0  0  0  0  0  X  0  X  0  0  0  X  X  0  0  X  0  0  X  X  X  0  X  X  X  X  0  0  X  0  X  0  X  X  X  0  0  X  X  0  0  0  0  0  X  X  X  0  X  X  X  0  X  0  0  0  0  X  X  0  0  0  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  0  0  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  0  0  X  X  X  X  X  0  0  0  0  X  0  X  0  X  X  X  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+190x^56+180x^58+356x^60+226x^62+317x^64+176x^66+228x^68+116x^70+126x^72+60x^74+48x^76+10x^78+6x^80+8x^84

The gray image is a linear code over GF(2) with n=128, k=11 and d=56.
This code was found by Heurico 1.16 in 1.79 seconds.