The generator matrix

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

generates a code of length 65 over Z2[X]/(X^2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+95x^58+157x^60+176x^62+178x^64+113x^66+89x^68+65x^70+49x^72+34x^74+26x^76+27x^78+8x^80+2x^82+4x^84

The gray image is a linear code over GF(2) with n=130, k=10 and d=58.
This code was found by Heurico 1.16 in 0.189 seconds.