The generator matrix

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

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+44x^46+88x^47+124x^48+178x^49+248x^50+272x^51+256x^52+260x^53+227x^54+264x^55+277x^56+264x^57+243x^58+264x^59+240x^60+152x^61+189x^62+148x^63+104x^64+94x^65+65x^66+48x^67+19x^68+12x^69+8x^70+4x^71+2x^72+1x^76

The gray image is a linear code over GF(2) with n=112, k=12 and d=46.
This code was found by Heurico 1.16 in 1.83 seconds.