The generator matrix

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

generates a code of length 56 over Z2[X]/(X^2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+54x^46+78x^47+124x^48+220x^49+215x^50+238x^51+256x^52+268x^53+244x^54+256x^55+284x^56+272x^57+251x^58+240x^59+231x^60+154x^61+199x^62+166x^63+102x^64+98x^65+58x^66+42x^67+21x^68+10x^69+3x^70+4x^71+5x^72+2x^73

The gray image is a linear code over GF(2) with n=112, k=12 and d=46.
This code was found by Heurico 1.10 in 0.657 seconds.