The generator matrix

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

generates a code of length 56 over Z2[X]/(X^2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+158x^50+189x^52+182x^54+109x^56+120x^58+73x^60+74x^62+56x^64+38x^66+16x^68+4x^70+2x^72+2x^76

The gray image is a linear code over GF(2) with n=112, k=10 and d=50.
This code was found by Heurico 1.16 in 0.577 seconds.