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  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  0  X  0  0  X  X  0  0  X  X  0  X  X  0  0  X  X  0  0  X  X  0  X  0  X  X  X  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0  X  0  X  X  0  0
 0  0  X  0  0  0  0  0  0  0  X  0  X  X  0  0  X  X  0  X  0  X  0  X  X  0  0  X  X  0  X  X  X  X  0  0  0  0  X  X  0  X  X  0  X  X  X  X  X  0  0  0  X  X  X  0  0  0
 0  0  0  X  0  0  0  0  0  0  X  0  X  0  X  X  X  0  0  0  X  X  X  X  0  0  X  0  X  X  X  0  0  X  X  0  X  X  X  X  X  X  X  X  0  0  0  0  0  0  0  X  0  X  X  X  0  0
 0  0  0  0  X  0  0  0  X  X  0  X  0  0  0  X  0  X  X  0  X  X  X  X  0  0  X  X  0  0  0  X  X  0  0  X  X  0  0  X  0  X  X  0  0  X  X  0  0  X  0  0  X  X  X  0  0  0
 0  0  0  0  0  X  0  X  X  X  0  0  0  0  0  0  X  X  0  X  X  0  X  X  0  X  X  0  0  X  0  0  X  X  X  0  0  X  X  0  X  0  X  0  X  0  0  X  X  X  0  0  X  X  0  0  0  0
 0  0  0  0  0  0  X  X  0  X  0  X  0  0  X  0  X  0  X  0  X  X  0  X  X  X  X  X  X  X  X  X  X  X  0  0  X  0  0  X  X  0  X  0  X  0  0  X  0  0  X  X  X  0  0  X  0  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+19x^52+44x^56+128x^58+44x^60+19x^64+1x^116

The gray image is a linear code over GF(2) with n=116, k=8 and d=52.
This code was found by Heurico 1.16 in 0.0408 seconds.