The generator matrix

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

generates a code of length 65 over Z2[X]/(X^2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+72x^57+160x^58+148x^59+114x^60+158x^61+170x^62+120x^63+119x^64+116x^65+123x^66+110x^67+74x^68+94x^69+98x^70+84x^71+54x^72+48x^73+68x^74+44x^75+12x^76+18x^77+20x^78+4x^79+10x^80+4x^81+1x^82+2x^83+2x^85

The gray image is a linear code over GF(2) with n=130, k=11 and d=57.
This code was found by Heurico 1.16 in 77.4 seconds.