The generator matrix

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

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+242x^52+343x^54+299x^56+234x^58+228x^60+175x^62+174x^64+110x^66+67x^68+38x^70+10x^72+3x^74+3x^76

The gray image is a linear code over GF(2) with n=116, k=11 and d=50.
This code was found by Heurico 1.16 in 0.527 seconds.