The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  X  1  1  0  1  1  0  1  1  0  1  X  1  1  1  0  1  1  0  1  1  0  0  1  1  1  X  1  1  X  1  0  0  1  1  1  X  0  1  1  1  X  0  0
 0  1  1  0  1  1  0  1  1  X X+1  1  0 X+1  1 X+1  0  1  0 X+1  1 X+1  1  0 X+1  1  1  X X+1  1  0  1  1  1  0  X X+1  1  0 X+1  1  0  1  1  1  1  X  1  1 X+1  0  X  1  1  1
 0  0  X  0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  X  X  X  X  0  X  X  0  X  X  X  X  X  X  0  X  0  0  0  0  X  0  X  0  0  X  X  X  0  X  0  0  0  X  X
 0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  X  0  X  0  X  X  X  X  0  X  0  X  0  X  0  0  X  X  X  X  X  X  X  X  0  X  X
 0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  0  X  0  0  0  X  X  0  X  X  0  X  0  0  X  X  0  0  X  X  X  X  X  X  X  X  X  X  X  X  X  X  0  X  0  0  X  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  0  X  X  X  X  X  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  X  0  X  0  0  0  X  0  0  0  0  X  X  X  X  0  X  0
 0  0  0  0  0  0  X  0  0  X  0  0  X  X  0  X  X  0  X  X  X  X  X  X  X  0  0  0  X  X  0  0  0  0  0  X  0  X  0  0  X  0  0  X  X  0  X  X  X  X  0  0  X  X  0
 0  0  0  0  0  0  0  X  0  0  X  0  X  0  0  X  X  0  0  X  0  0  0  X  X  X  X  X  0  X  0  0  0  0  X  X  0  X  X  X  0  0  X  X  X  X  0  X  0  X  0  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  0  X  0  X  X  X  0  0  0  X  X  0  X  X  0  X  0  X  0  0  X  0  0  0  X  X  0  0  X  X  X  X  0  0  0  X  0  X  0  X  0  0  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+77x^46+189x^48+203x^50+297x^52+294x^54+280x^56+268x^58+184x^60+149x^62+48x^64+23x^66+13x^68+8x^70+10x^72+2x^74+2x^76

The gray image is a linear code over GF(2) with n=110, k=11 and d=46.
This code was found by Heurico 1.16 in 37.2 seconds.