The generator matrix

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

generates a code of length 64 over Z2[X]/(X^2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+104x^53+171x^54+224x^55+309x^56+354x^57+412x^58+430x^59+405x^60+458x^61+543x^62+498x^63+495x^64+470x^65+462x^66+498x^67+464x^68+436x^69+369x^70+288x^71+236x^72+182x^73+140x^74+94x^75+67x^76+42x^77+13x^78+14x^79+6x^80+2x^81+2x^82+2x^83+1x^88

The gray image is a linear code over GF(2) with n=128, k=13 and d=53.
This code was found by Heurico 1.10 in 3.08 seconds.