The generator matrix

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

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+144x^46+461x^48+454x^50+536x^52+492x^54+512x^56+490x^58+470x^60+262x^62+167x^64+72x^66+26x^68+6x^70+2x^72+1x^80

The gray image is a linear code over GF(2) with n=110, k=12 and d=46.
This code was found by Heurico 1.16 in 1.79 seconds.