The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  1  0  X  0  1  0  1  1  1  X  0  0  1  0  0  X  1  1  X  0  1  1  1  1  1  0  1  X  X  0  X  1  0  1  1  1  1  1  0
 0  1  0  0  0  1  1  1  0  X X+1 X+1  1  1  X  0  0  0  1  X  1 X+1  1  1  0  0  0  0  1  1  X  0  X  X  1  0  X X+1 X+1 X+1  0 X+1  1  1  1  1  0  0  X X+1  1  X  0  X
 0  0  1  0  1  1  0  1  0  1  1  X  0  1  1  X  1  X  X  1  1 X+1  0  1  1  1  1  0 X+1  0  0  1 X+1  1 X+1  0  X  0  0  X  1  X  X X+1  1  0  0  X  1  0  0  1  X  X
 0  0  0  1  1  0  1  1  1  0 X+1  X  1  X  1 X+1  0  1  0 X+1  0  0  1 X+1  0  X  1  X X+1  1  1  X X+1  1 X+1  0  0  X  1 X+1 X+1  1 X+1  0  1  1 X+1  1 X+1  X  0  0  1  1
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  X  X  0  X  X  0  X  0  X  X  0  0  0  X  0  0  0  X  X  X  X  X  0  X  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  X  X  X  X  0  0  0  X  0  0  X  X  0  X  0  X  0  X  X  0  0  0  X  X  0  X  X  0  X  X  X  X  0  0  0  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  0  X  X  0  0  X  0  X  X  0  X  X  0  0  0  0  X  X  0  0  X  0  0  0  X  X  X  0  0  X  X  0  X  X  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  X  X  0  X  X  0  0  X  X  X  X  0  0  X  0  0  0  0  X  X  0  X  X  0  X  0  0  0  0  X  X  X  X  X  0  X  X  X  X  0  X  0
 0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  0  0  0  X  0  0  X  0  0  X  0  0  X  0  X  0  X  0  0  0  X  X  X  0  X  0  X  0  X  0  X  X  0  X  0  X  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+259x^44+482x^46+855x^48+896x^50+1076x^52+1052x^54+1117x^56+952x^58+797x^60+402x^62+214x^64+56x^66+26x^68+4x^72+2x^76+1x^88

The gray image is a linear code over GF(2) with n=108, k=13 and d=44.
This code was found by Heurico 1.16 in 59.9 seconds.