The generator matrix

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

generates a code of length 56 over Z2[X]/(X^2) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+56x^45+177x^46+156x^47+276x^48+318x^49+403x^50+424x^51+479x^52+490x^53+455x^54+604x^55+501x^56+588x^57+524x^58+544x^59+477x^60+428x^61+363x^62+260x^63+257x^64+150x^65+108x^66+56x^67+51x^68+18x^69+13x^70+4x^71+5x^72+4x^74+1x^82+1x^92

The gray image is a linear code over GF(2) with n=112, k=13 and d=45.
This code was found by Heurico 1.16 in 68.2 seconds.