The generator matrix

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

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+66x^46+76x^47+135x^48+196x^49+243x^50+244x^51+260x^52+274x^53+221x^54+258x^55+250x^56+268x^57+211x^58+272x^59+236x^60+196x^61+169x^62+132x^63+152x^64+72x^65+73x^66+36x^67+20x^68+18x^69+8x^70+6x^71+2x^72+1x^82

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 1.79 seconds.