The generator matrix

1 0 0 0 0 0 1 1 1 X 1 1 0 0 1 1 1 1 X 1 X 1 X 1 1 X 0 X X X 0 0 1 0 0 1 1 X 1 0 1 X X 1 1 1 1 1 1 X 1 0 0 1
0 1 0 0 0 0 0 0 0 0 0 0 X 1 1 X+1 1 X+1 1 X+1 X X 1 X+1 1 1 1 X 1 X 1 1 X 0 1 X 0 X X X 0 1 X 1 1 1 X X X+1 0 1 1 0 0
0 0 1 0 0 0 0 0 X X 1 1 1 X 0 0 X+1 X+1 X+1 1 1 1 1 X X+1 X 1 1 X+1 X 1 0 1 1 0 X 0 0 X+1 0 X 0 1 0 X X 0 0 1 1 X X 0 0
0 0 0 1 0 0 1 X 1 1 0 X+1 1 1 X X+1 X+1 0 0 1 1 X X X 0 1 X+1 0 X+1 1 0 X+1 1 X 0 0 X 1 X+1 1 X 1 X+1 X X 1 X 0 X+1 1 1 X+1 1 0
0 0 0 0 1 0 1 X+1 0 1 X X+1 1 1 0 1 0 X 1 1 0 X+1 X 1 X+1 X X+1 X+1 X X+1 1 X+1 1 X X X+1 1 X X X+1 1 1 1 0 X X+1 X+1 0 X X+1 1 X X+1 0
0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 X X+1 1 1 X 0 0 1 X 1 X X+1 1 1 1 1 X X+1 X+1 X X+1 1 0 X+1 1 X+1 X 0 X 1 1 X+1 0 X+1 1 X+1 1 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+46x^44+82x^45+178x^46+180x^47+198x^48+236x^49+259x^50+280x^51+242x^52+264x^53+247x^54+274x^55+236x^56+278x^57+217x^58+190x^59+208x^60+132x^61+117x^62+90x^63+49x^64+30x^65+36x^66+10x^67+12x^68+2x^69+2x^70

The gray image is a linear code over GF(2) with n=108, k=12 and d=44.
This code was found by Heurico 1.10 in 0.641 seconds.