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 X X X X X X 0 X X 1 1 X 1 1 X X 1
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 X 0 X 0 X X X X 0 0 X 0 0 X X X 0 X X 0 X 0 0 0 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 X 0 X 0 0 0 X X X 0 0 0 0 X X 0 X X 0 0 X 0 0 0 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 X X 0 X X 0 0 0 X 0 0 0 X X X 0 X 0 X X 0 X 0 0 X 0 0 X 0 0
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 0 0 0 0 X X X X 0 0 0 X 0 0 0 X X X 0 0 X 0 X 0 X X 0 X 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 0 X X 0 0 0 0 0 0 X X 0 X X 0 0 0 X 0 0 X X X 0 X 0 X 0 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 0 0 X X 0 0 X X 0 0 X 0 X X 0 X 0 X 0 0 0 X X X 0 X X
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 X X X 0 X 0 X X X 0 0 X 0 0 X 0 X X 0 0 0 0 X 0 0 X 0 X 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 X 0 X X X 0 X X X 0 X X X X 0 X X 0 0 0 X 0 0 0 X X 0 X X 0
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 0 0 X X 0 X X X X 0 X 0 0 0 0 0 0 0 0 X X X X X X X 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 X 0 0 0 X 0 0 0 0 0 X 0 X X 0 0 X 0 X 0 0 X 0 0 0 X 0 X 0
generates a code of length 56 over Z2[X]/(X^2) who´s minimum homogenous weight is 44.
Homogenous weight enumerator: w(x)=1x^0+182x^44+372x^48+132x^50+554x^52+368x^54+875x^56+408x^58+580x^60+112x^62+303x^64+4x^66+154x^68+48x^72+2x^76+1x^88
The gray image is a linear code over GF(2) with n=112, k=12 and d=44.
This code was found by Heurico 1.16 in 6.76 seconds.