The generator matrix

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

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+203x^44+596x^46+766x^48+954x^50+1035x^52+1132x^54+1065x^56+922x^58+779x^60+418x^62+222x^64+68x^66+23x^68+6x^70+1x^72+1x^80

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 7.6 seconds.