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 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X X X 1 X X X X X
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X X 0 X X 0 X X 0 X X X X X X X 0 0 0 X X X 0
0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X X X X 0 0 0 X 0 X 0 0 X X 0 0 0 X X X X X X 0 X X 0 X X 0 X X 0
0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 0 0 0 X 0 X X 0 0 X X X 0 0 0 0 X X 0 0 X X X 0 X 0 X X X X X
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X X X 0 X X 0 X X X 0 0 0 X 0 0 0 X 0 X X X X X X X 0 0 X 0 0 X 0 X 0 0 X
0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X 0 X X 0 X 0 X 0 X X X X 0 0 0 X X 0 0 X 0 0 X X X 0 0 X 0 X 0 X X 0 X 0 X 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X 0 X X 0 X 0 X 0 0 X 0 X 0 X 0 0 X 0 X 0 0 X 0 X X 0 0 0 0 X X 0 X X 0
0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X 0 X 0 0 0 X X X 0 0 X 0 X 0 X 0 0 X X X 0 0 X X 0 X 0 X X X 0 X X X 0 X X
0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X 0 X 0 0 X 0 0 0 0 X X X 0 0 X X X X X X 0 0 X X 0 X 0 0 X X 0 X 0 0 0 X
0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 0 0 X 0 0 X X 0 0 X 0 X X 0 X X X 0 0 0 0 X X 0 X X 0 0 0 X 0 0 0 X X 0 0 X
0 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X X X X X 0 X 0 X 0 0 0 0 0 0 0 0 X 0 0 X X 0 0 0 X X X X 0 X 0 X 0 0 0 X X
generates a code of length 55 over Z2[X]/(X^2) who´s minimum homogenous weight is 42.
Homogenous weight enumerator: w(x)=1x^0+68x^42+140x^44+156x^46+205x^48+355x^50+533x^52+626x^54+605x^56+469x^58+348x^60+248x^62+142x^64+93x^66+66x^68+26x^70+7x^72+7x^74+1x^84
The gray image is a linear code over GF(2) with n=110, k=12 and d=42.
This code was found by Heurico 1.16 in 9.53 seconds.