The generator matrix

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

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+213x^46+309x^48+545x^50+451x^52+624x^54+457x^56+562x^58+365x^60+293x^62+174x^64+61x^66+29x^68+6x^70+3x^72+3x^76

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 6.54 seconds.