The generator matrix

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

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+234x^56+422x^58+537x^60+476x^62+488x^64+436x^66+444x^68+354x^70+342x^72+184x^74+115x^76+42x^78+15x^80+6x^82

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 12.4 seconds.