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.