The generator matrix

 1  0  0  0  1  1  1  1  1  0  X  0  1  X  1  1  1  1  1  X  0  X  1  X  1  1  X  0  1  1  1  1  X  0  0  1  1  X  X  1  1  X  0  X  1  1  X  1  0  1  0  X  0  0  X  1  0  1  X  1  X  X  1  1
 0  1  0  0  0  1  1  X  0  0  1  1  1  1  X  X X+1  0 X+1  X  1  1  X  1  1  1  0  X  1 X+1  X X+1  0  1  0  X  0  1  1  0 X+1  X  1  X  X X+1  0  0  0 X+1  1  1  1  X  1  0  0  0  X X+1  0  X  X X+1
 0  0  1  0  1  1  0  0 X+1  1  X  1  1  1  0  1 X+1  X  0  X  1  X X+1  X X+1  X  1  1  X  X  1 X+1  1 X+1  X  0  X  1  X  0  1  X X+1  1  1 X+1  1 X+1  1 X+1  1  1 X+1  1  1  1  1  1  0  0  0  0  0  1
 0  0  0  1  1  0  1  1  0 X+1 X+1  1 X+1  X  1 X+1  1  X  X  1 X+1  0  X  1  X  1  1  X  X  X  1 X+1  0  1  1  0 X+1 X+1 X+1  0 X+1  1 X+1  0 X+1  X  1  X  0  0  0  1 X+1  X  1 X+1  1  X  1  1  1  1 X+1  X
 0  0  0  0  X  0  0  0  X  X  0  X  X  0  X  0  0  X  X  0  X  X  0  X  X  X  X  0  X  0  X  0  0  0  0  0  X  X  0  X  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  0  X  0  0  X  X  X  0  X
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  0  X  0  X  0  X  X  X  X  X  X  0  X  0  0  X  0  0  X  0  X  X  0  X  0  0  0  0  0  X  X  X  0  X  X  0  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  X  X  0  X  X  X  X  X  X  X  X  X  X  X  X  0  0  X  X  0  0  0  0  0  X  X  X  0  X  X  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+163x^56+260x^58+294x^60+268x^62+251x^64+202x^66+208x^68+154x^70+111x^72+58x^74+50x^76+18x^78+10x^80

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 0.595 seconds.