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.