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 X X 1 1 1 1 1 1 1 1 X X 1 1 1 1 1 X 1 X 1 0 1 1 1 X X 1 1 1 1 0 1 X X
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 X 0 X 0 X X X X 0 X X 0 X 0 0 0 0 0 0 X 0 0 0 0 0 0 X X X X 0 X 0 X X X 0 0 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 0 X X 0 0 X X X X X 0 0 0 0 0 X X X 0 X 0 X 0 X X 0 X 0 0 X 0 0 X 0 X 0 0 X X
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 0 0 X X X X 0 0 X 0 X 0 0 X X 0 0 0 0 0 X 0 X 0 0 X X 0 0 X 0 0 X X X 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 0 X 0 X 0 0 X 0 X X 0 0 X X X X 0 0 X X X 0 0 0 0 0 0 0 X 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 X X X X 0 X 0 0 0 X X 0 0 X 0 0 X X X X 0 0 X 0 X X 0 0 X X 0 X X X 0 X X X 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 X X X 0 0 X 0 X 0 X 0 0 X 0 0 0 X X 0 0 X X 0 X 0 0 X X 0 0 X 0 X X 0 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 X 0 0 0 0 0 X X X 0 X X X 0 0 X 0 0 0 0 X X X 0 0 0 0 X 0 0 0 0 X 0 X 0 X 0 0
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 X X 0 0 0 X 0 X 0 X X 0 0 X 0 0 X 0 X X X 0 X 0 X X 0 X 0 X 0 X 0 X 0 X 0 X
generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 58.
Homogenous weight enumerator: w(x)=1x^0+40x^58+74x^60+105x^62+88x^64+156x^66+158x^68+118x^70+115x^72+45x^74+46x^76+29x^78+18x^80+14x^82+10x^84+4x^86+1x^88+1x^90+1x^112
The gray image is a linear code over GF(2) with n=136, k=10 and d=58.
This code was found by Heurico 1.16 in 1.44 seconds.