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

generates a code of length 55 over Z2[X]/(X^2) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+174x^46+359x^48+506x^50+581x^52+498x^54+518x^56+500x^58+387x^60+252x^62+209x^64+78x^66+24x^68+8x^70+1x^72

The gray image is a linear code over GF(2) with n=110, k=12 and d=46.
This code was found by Heurico 1.10 in 0.656 seconds.