The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  0  0  X  1  1  1  X  1  0  1  1  0  1  0  X  0  1  1  1  1  X  1  1  1  0  0  X  0  0  0  0  1  X  1  1  1  X  0  1  1  0  X  1  1  X
 0  1  0  0  0  0  0  0  0  1  1  1  1  1  1  X X+1  X  0  1 X+1 X+1  X  X  1  1  1  1 X+1  1 X+1  0 X+1  0  X  X  1  1  1  X  1  0  0  1 X+1  1  1  X  1  X  X  1  1  X  X  0
 0  0  1  0  0  0  1  1  1  1  X  1  0 X+1 X+1 X+1  X  1  X  0  1  0  0 X+1 X+1  1  X  1  X  1  1  1  0 X+1  0  1 X+1  X  0  X X+1  1  X  1  1  0  1  0 X+1  1 X+1  1  0  X  X  X
 0  0  0  1  0  1  1  0  1  0 X+1 X+1  1  X X+1 X+1  X  X  X  X  0 X+1  1  1 X+1  0  1  X X+1  1 X+1 X+1  X  X X+1 X+1  0  1 X+1  1  1  0 X+1 X+1  X  1  X  X X+1  1  X  1  X  0  0  X
 0  0  0  0  1  1  0  1  1  X  0  X  1 X+1 X+1  0 X+1 X+1 X+1  1  1  1  0  1 X+1  0  0 X+1 X+1 X+1  0  X  0  0  0  X  X X+1  0  1  1  X  1  1  X  X  1  1  X  0  X X+1  1  X X+1  0
 0  0  0  0  0  X  0  0  0  X  0  X  X  0  X  X  0  0  X  X  X  X  X  X  0  0  X  0  0  0  0  X  X  X  X  0  0  X  X  X  0  X  X  X  X  0  0  0  0  0  0  X  X  0  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  0  0  X  X  X  0  X  0  X  X  X  X  X  X  0  0  X  0  0  X  0  0  0  X  X  0  X  X  0  X  0  X  X  X  0  0  X  X  X  X  0
 0  0  0  0  0  0  0  X  0  0  X  X  X  0  X  0  X  X  X  0  0  X  X  X  X  X  0  0  0  X  0  X  X  X  0  X  X  0  X  X  X  X  0  X  0  0  X  X  0  0  0  X  X  X  X  0
 0  0  0  0  0  0  0  0  X  X  X  0  X  X  X  X  0  0  X  0  0  X  0  X  X  0  0  0  0  X  X  0  0  X  0  0  X  X  0  X  0  X  X  0  0  0  X  X  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 44.

Homogenous weight enumerator: w(x)=1x^0+211x^44+520x^46+1044x^48+1268x^50+1764x^52+2098x^54+2382x^56+2240x^58+1955x^60+1332x^62+892x^64+412x^66+174x^68+66x^70+16x^72+8x^76+1x^80

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 56.9 seconds.