The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  X  1  1  1  1  1  1  X  1  1  X  X  1  X  1  X  1  1  X  X  X  1
 0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  0  0  0  0  X  X  X  X  0  X  X  0  X  0  X  X  X  X  0  X  0  0  X  X  0  0  0  X  0  X  X  X  0  X  X  X  X  X  0
 0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  0  X  X  0  0  0  0  0  0  X  X  X  0  0  0  X  X  X  X  0  X  X  X  0  X  X  0  0  0  0  0  X  X  X  X  0  0
 0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  0  X  0  X  X  X  X  0  X  0  X  0  X  0  0  0  X  0  0  X  X  0  0  X  X  X  X  0  X  0  0  0  X  0  0  0  0  X
 0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  X  0  0  0  0  0  X  X  0  X  X  0  X  X  0  X  0  0  0  X  X  0  0  0  0  X  0  X  0  0  X  0  X  X  0  X
 0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  X  0  X  X  X  0  0  X  0  X  X  X  X  0  X  X  0  X  0  0  X  0  0  X  0  X  X  0  0  0  0  X  0  X  0  X  0  0  0
 0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  X  X  0  X  X  0  X  X  0  0  X  0  0  0  X  0  X  0  0  X  X  X  0  X  X  X  0  0  0  X  0  0  0  X  X  X  X  0  0
 0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  0  X  X  X  X  X  0  X  X  0  X  X  0  X  X  0  0  0  X  0  0  0  0  X  0  X  0  0  X  X  0  X  0  X  X  X  X  X
 0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0  0  0  X  0  0  0  X  0  X  0  0  X  0  X  0  0  0  0  X  0  X  0  X  X  X  0  X  X  0  X  0  X  X  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+70x^46+120x^48+42x^50+80x^52+220x^54+197x^56+84x^58+48x^60+78x^62+55x^64+2x^66+16x^70+10x^72+1x^88

The gray image is a linear code over GF(2) with n=110, k=10 and d=46.
This code was found by Heurico 1.16 in 14.7 seconds.