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
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  X  X  0  X  X  0  X  0  X  0  0  X  X  X  0  0  0  X  X  X  0  0  X  0  X  0  X  X  0  X  0  X  X  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  X  X  X  0  X  X  0  X  X  0  X  X  0  0  X  X  X  0  0  X  X  X  0  0  X  X  X  0  0  0  0  X  X  0  X  X  X  X  X  X  X  0  0
 0  0  0  X  0  0  0  0  0  0  0  X  X  X  0  0  0  0  X  X  X  X  X  X  0  X  0  0  0  X  0  X  X  0  X  X  0  X  X  0  0  X  0  X  X  0  X  0  X  0  X  X  0  0  0  X  0
 0  0  0  0  X  0  0  0  X  X  X  X  X  0  0  X  X  X  0  X  0  0  0  0  0  X  X  0  0  X  X  0  X  0  0  0  X  X  0  X  X  X  0  0  0  0  X  X  X  X  X  0  0  X  X  X  0
 0  0  0  0  0  X  0  X  X  X  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  0  X  X  0  0  X  X  X  X  0  X  X  X  X  X  X  X  X  X  0  0  X  0  X  0  0  X  X  0  X  0
 0  0  0  0  0  0  X  X  0  X  X  0  X  X  0  0  0  0  X  0  X  0  0  X  X  0  X  0  X  0  X  0  X  0  X  X  0  0  0  0  X  X  X  0  X  X  0  X  X  0  X  X  0  X  X  X  0

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+19x^52+17x^54+27x^56+128x^57+27x^58+17x^60+19x^62+1x^114

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.