The generator matrix

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

generates a code of length 53 over Z2[X]/(X^2) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+154x^44+394x^46+482x^48+546x^50+526x^52+518x^54+512x^56+384x^58+339x^60+148x^62+60x^64+26x^66+5x^68+1x^72

The gray image is a linear code over GF(2) with n=106, k=12 and d=44.
This code was found by Heurico 1.10 in 0.625 seconds.