The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  X  1  0  1  0  0  1  X  1  1  X  0  X  1  1  X  1  X  1  1  0  1  X  1  1  X  X  1  1  1  X  1  X  1  1  0  X  1  0  X  0  1  1
 0  1  0  0  0  0  0  0  0  1  1  1  1  1 X+1  X  1  1  1  1  X  0  1  0  X  0  1 X+1  1  0 X+1  1  1  0 X+1  1  0  1  X  1  X  0  1  X  1 X+1  1  1  X  X  1  1  0 X+1
 0  0  1  0  0  0  1  1  1  1 X+1  0  0 X+1  X  0 X+1  1  X X+1  0  1  X  1  0 X+1 X+1  0  1  X  X  0 X+1  1  1  0  1  X X+1  0  0  X  1  1  X X+1  1  X  X  1  X X+1  X  X
 0  0  0  1  0  1  1  0  1  X X+1  1  0  1  1  X  X  X X+1  1  1 X+1  X  X  0  1  0  0  0 X+1  1 X+1  1  1 X+1  1  0  0  X  X  1  1  0  0  X  X X+1  0  1 X+1 X+1  1  0 X+1
 0  0  0  0  1  1  0  1 X+1  X X+1 X+1  1  X  0  1  1  0 X+1  1 X+1  1  X  0  0 X+1  1  1  X  0  1  0  X  X  X X+1  1 X+1  0  0 X+1  X X+1  0  X  0  1  X  1 X+1  0  0  1  0
 0  0  0  0  0  X  0  0  X  0  X  X  X  X  0  X  0  X  0  0  0  0  X  X  X  X  X  X  0  0  0  X  0  X  X  0  X  0  X  0  0  X  0  0  X  0  0  0  X  0  0  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  0  0  X  0  0  X  X  0  0  X  0  X  0  X  X  X  0  0  X  0  X  X  X  X  X  X  0  0  0  X  0  0  X  0  X
 0  0  0  0  0  0  0  X  0  0  0  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  X  X  X  X  0  X  X  X  X  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+227x^44+566x^46+801x^48+914x^50+1035x^52+1118x^54+1019x^56+1004x^58+772x^60+442x^62+222x^64+50x^66+13x^68+2x^70+5x^72+1x^92

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 7.7 seconds.