The generator matrix

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

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+58x^44+186x^45+317x^46+400x^47+448x^48+578x^49+710x^50+754x^51+922x^52+1028x^53+1064x^54+1146x^55+1122x^56+1110x^57+1120x^58+1074x^59+926x^60+804x^61+737x^62+578x^63+406x^64+352x^65+242x^66+132x^67+78x^68+38x^69+34x^70+12x^71+6x^72+1x^96

The gray image is a linear code over GF(2) with n=112, k=14 and d=44.
This code was found by Heurico 1.10 in 9.44 seconds.