The generator matrix

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

generates a code of length 58 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+242x^52+361x^56+186x^60+141x^64+74x^68+17x^72+2x^76

The gray image is a linear code over GF(2) with n=116, k=10 and d=52.
This code was found by Heurico 1.10 in 0.593 seconds.