The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  X  X  X  X  X
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  0  X  X  X  X  0  0  X  X  X  X  0  0  X  X  0  X  X  0  X  X  0  0  X  X  X  X  0  0  X  X  X  X
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  X  X  0  X  X  0  X  0  X  X  X  0  0  X  X  X  X  0  X  X  0  X  0  X  X  X  X  X  X  0  X  0  X  0  0  0
 0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  X  X  X  X  0  X  0  0  X  0  X  X  0  X  X  0  0  X  0  X  X  0  X  X  X  0  0  0  0  0  X  X  0  X  X  X  X  X  0
 0  0  0  0  X  0  0  0  X  X  X  X  X  0  X  X  0  0  0  0  0  0  0  0  0  0  0  X  X  0  X  X  X  0  X  X  X  0  X  X  0  0  X  X  0  0  X  X  0  X  X  X  X  0  0  0  0  X
 0  0  0  0  0  X  0  X  X  X  0  0  0  0  X  X  X  X  0  0  0  0  0  0  0  0  X  X  0  X  X  0  X  X  0  X  0  X  0  X  X  X  0  X  0  X  0  X  X  0  X  0  0  0  X  0  X  X
 0  0  0  0  0  0  X  X  0  X  X  0  X  X  X  0  0  X  0  0  0  0  X  X  X  X  X  0  X  X  0  0  X  0  X  X  X  0  X  X  X  X  0  X  X  0  X  0  0  0  0  0  0  0  X  0  0  X

generates a code of length 58 over Z2[X]/(X^2) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+14x^53+32x^54+48x^56+70x^57+42x^61+28x^62+15x^64+2x^65+3x^70+1x^102

The gray image is a linear code over GF(2) with n=116, k=8 and d=53.
This code was found by Heurico 1.16 in 0.406 seconds.