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.