The generator matrix

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

generates a code of length 54 over Z2[X]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+231x^44+506x^46+887x^48+882x^50+1068x^52+1068x^54+1130x^56+880x^58+785x^60+438x^62+230x^64+62x^66+19x^68+4x^70+1x^84

The gray image is a linear code over GF(2) with n=108, k=13 and d=44.
This code was found by Heurico 1.10 in 2.45 seconds.