The generator matrix

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

generates a code of length 65 over Z2[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+36x^56+66x^57+92x^58+140x^59+173x^60+150x^61+134x^62+160x^63+132x^64+126x^65+89x^66+82x^67+120x^68+90x^69+68x^70+78x^71+80x^72+64x^73+42x^74+34x^75+27x^76+16x^77+22x^78+18x^79+7x^80+1x^82

The gray image is a linear code over GF(2) with n=130, k=11 and d=56.
This code was found by Heurico 1.16 in 0.593 seconds.