The generator matrix

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

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+154x^50+188x^52+166x^54+156x^56+88x^58+101x^60+62x^62+42x^64+34x^66+15x^68+8x^70+9x^72

The gray image is a linear code over GF(2) with n=112, k=10 and d=50.
This code was found by Heurico 1.10 in 4.34 seconds.