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 0 X 1 X X X X 1 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 0 X X 0 X X 0 X X 0 X X X X X X X 0 0 0 0 X 0 X 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 0 0 X 0 X 0 0 X X 0 0 0 X X X X X X 0 X X 0 0 X 0 0 0 0 0 0 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 0 0 0 X 0 X 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 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 X 0 X X 0 0
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 0 0 0 0 X X X 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 X 0 X 0 X 0 0 X 0 X 0 0 X 0 X X 0 0 0 X 0 0 0 0 X X X 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 0 0 X 0 X 0 X 0 0 X X X 0 0 X X 0 X 0 X X X X 0 X 0 0 0 0 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 0 X X 0 0 X 0 0 0 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 X 0 X X X 0 0 0 0 X X 0 X X 0 0 0 X 0 0 X 0 X 0 0 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 0 0 0 0 0 0 0 X 0 0 X X 0 0 0 X X X X 0 X X X X 0 X X 0 X X X
generates a code of length 58 over Z2[X]/(X^2) who´s minimum homogenous weight is 44.
Homogenous weight enumerator: w(x)=1x^0+97x^44+259x^48+46x^50+453x^52+250x^54+752x^56+444x^58+705x^60+228x^62+458x^64+54x^66+227x^68+2x^70+95x^72+22x^76+2x^80+1x^88
The gray image is a linear code over GF(2) with n=116, k=12 and d=44.
This code was found by Heurico 1.16 in 3.4 seconds.