The generator matrix

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

generates a code of length 54 over Z2[X]/(X^2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+82x^46+276x^48+328x^50+319x^52+242x^54+224x^56+178x^58+178x^60+108x^62+75x^64+22x^66+15x^68

The gray image is a linear code over GF(2) with n=108, k=11 and d=46.
This code was found by Heurico 1.10 in 0.172 seconds.