The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  X  1  1  0  1  0  1  1  0  1  1  1  0  X  1  1  1  1  0  0  1  X  1  1  X  0  1  X  1  1  1  1  1  X  X  1  X  1  0  1  0  1  1
 0  1  1  0  1  1  0  1  1  0 X+1  1  X X+1  1  0  1 X+1  X  1  0 X+1 X+1  1  1 X+1  0  X  1  1  1 X+1  1  1  0  1  1  1  1  0  1  1  1  0  1  1 X+1  1  0  X  0  0 X+1  0
 0  0  X  0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  0  X  X  0  X  X  X  0  X  0  0  X  0  0  0  0  X  X  X  X  0  0  X  X  0  0  0  X  0  X  0  X  0  0  X  X
 0  0  0  X  0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  X  0  X  X  X  X  X  X  X  0  X  X  X  0  X  0  X  0  X  0  X  0  X  X  0  0  0  X  0  X  X  0  X  X  0
 0  0  0  0  X  0  0  0  0  0  X  0  0  0  X  0  X  X  0  0  0  X  0  0  X  0  X  X  0  X  X  0  X  0  X  0  X  0  X  X  X  0  0  X  X  0  X  X  X  0  0  0  X  X
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  X  X  X  X  0  X  X  0  X  X  X  X  0  0  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  0  X  0  X  X  X  0  0  X  X  X  X  0  0  X  0  0  0  X  0  0  X  X  0  0  X  X  X  X  0  X  0  X  0  X  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  0  0  X  X  X  0  X  0  X  0  0  X  0  0  0  X  X  X  0  0  0  X  X  X  X  0  X  X  0  X  0  X  0  0  X  0  0  X  0  X  X  X
 0  0  0  0  0  0  0  0  X  0  0  X  0  X  X  0  X  X  0  X  0  X  X  0  0  0  0  0  X  X  0  X  X  0  0  0  0  X  0  X  X  0  0  X  X  X  0  0  0  0  X  X  X  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  0  0  X  X  X  X  0  X  0  X  X  0  0  X  X  0  0  0  X  X  X  X  0  0  0  0  0  X  X  0  0  X  0  0  X  X  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+197x^44+116x^46+467x^48+384x^50+643x^52+544x^54+614x^56+376x^58+442x^60+108x^62+142x^64+8x^66+43x^68+8x^72+3x^76

The gray image is a linear code over GF(2) with n=108, k=12 and d=44.
This code was found by Heurico 1.16 in 23.9 seconds.