The generator matrix

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

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+60x^58+193x^60+208x^62+143x^64+120x^66+87x^68+62x^70+51x^72+26x^74+26x^76+34x^78+9x^80+2x^82+2x^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 1.10 in 0.047 seconds.