The generator matrix

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

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+62x^44+188x^45+260x^46+390x^47+540x^48+578x^49+672x^50+818x^51+911x^52+1018x^53+1063x^54+1130x^55+1091x^56+1060x^57+1129x^58+1062x^59+971x^60+836x^61+727x^62+568x^63+456x^64+306x^65+218x^66+184x^67+60x^68+46x^69+26x^70+8x^71+4x^72+1x^98

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 59.2 seconds.