The generator matrix

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

generates a code of length 56 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+84x^52+108x^56+40x^60+19x^64+3x^68+1x^100

The gray image is a linear code over GF(2) with n=112, k=8 and d=52.
This code was found by Heurico 1.16 in 0.031 seconds.