The generator matrix

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

generates a code of length 65 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+165x^54+492x^56+747x^58+802x^60+914x^62+975x^64+1044x^66+978x^68+789x^70+616x^72+351x^74+191x^76+84x^78+36x^80+2x^82+4x^84+1x^92

The gray image is a linear code over GF(2) with n=130, k=13 and d=54.
This code was found by Heurico 1.10 in 3.11 seconds.