The generator matrix

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

generates a code of length 57 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+25x^52+18x^53+23x^54+42x^55+19x^56+30x^57+24x^58+14x^59+15x^60+14x^61+7x^62+6x^63+2x^64+2x^65+7x^66+2x^67+2x^70+1x^72+1x^74+1x^88

The gray image is a linear code over GF(2) with n=114, k=8 and d=52.
This code was found by Heurico 1.16 in 0.031 seconds.