The generator matrix

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

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+208x^52+100x^54+238x^56+64x^58+168x^60+46x^62+97x^64+22x^66+46x^68+22x^70+8x^72+2x^74+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 1.16 in 0.742 seconds.