The generator matrix

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

generates a code of length 56 over Z2[X]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+102x^44+158x^45+273x^46+354x^47+490x^48+646x^49+685x^50+816x^51+833x^52+1012x^53+1078x^54+1044x^55+1209x^56+1194x^57+1109x^58+1040x^59+950x^60+850x^61+695x^62+578x^63+393x^64+318x^65+225x^66+128x^67+107x^68+44x^69+24x^70+8x^71+11x^72+2x^73+5x^74+1x^78+1x^94

The gray image is a linear code over GF(2) with n=112, k=14 and d=44.
This code was found by Heurico 1.16 in 57.4 seconds.