The generator matrix

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

generates a code of length 58 over Z2[X]/(X^2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+121x^50+270x^52+303x^54+288x^56+258x^58+215x^60+199x^62+170x^64+102x^66+63x^68+38x^70+17x^72+3x^74

The gray image is a linear code over GF(2) with n=116, k=11 and d=50.
This code was found by Heurico 1.10 in 0.187 seconds.