The generator matrix

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

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+366x^56+160x^58+740x^60+240x^62+750x^64+260x^66+661x^68+208x^70+340x^72+120x^74+198x^76+32x^78+15x^80+4x^82+1x^84

The gray image is a linear code over GF(2) with n=130, k=12 and d=56.
This code was found by Heurico 1.16 in 48.1 seconds.