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 1 1 1 1 1 1 1 X X X X X X X X X 1 1 1 X 0 X X X 1 1 X 1 1 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 X X 0 X 0 0 0 X X X 0 X X X 0 X 0 X 0 X 0 X 0 0 X X X 0 0 X X 0 X 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 0 0 X X X 0 0 0 X X X X 0 X 0 0 X X X 0 0 X 0 0 0 X 0 X 0 0 X X X 0 X X 0 0 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 X 0 X 0 0 X X 0 0 0 X X X 0 X 0 X X X X X 0 X 0 X 0 X X X X X X X 0 X 0 X 0 0 0 X 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 X X X X 0 X X 0 0 0 0 X 0 0 0 X 0 0 0 0 0 X X 0 0 0 X 0 0 0 X X 0 X 0 X X X 0 X 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 X X 0 0 0 X 0 X 0 0 0 X 0 X 0 X X X X 0 0 X 0 X 0 X X X X X 0 X X 0 X 0 0 0 0 X 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 0 X X X 0 0 0 0 X 0 0 X 0 X X X 0 X 0 0 X 0 0 0 X 0 0 X 0 X X 0 0 0 0 X 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 X X X 0 0 0 X X X X X 0 0 0 0 X X X X 0 X 0 0 0 X X X 0 0 X X 0 0 0 X X 0 0 X X X 0
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 0 X X X X 0 0 X 0 X X X 0 X X X X 0 X 0 X 0 0 X 0 0 X X 0 X 0 X X 0 X 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 0 X X 0 X X 0 0 0 0 X 0 0 0 X 0 X 0 X X 0 0 0 0 X X 0 0 X X X X 0 X X X 0 0 X 0 0 0
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 X 0 X 0 0 X 0 X X 0 0 X 0 0 0 X 0 0 0 0 X X X X X X 0 X 0 0 0 X X X 0 0 X 0 0 0 X X
generates a code of length 73 over Z2[X]/(X^2) who´s minimum homogenous weight is 58.
Homogenous weight enumerator: w(x)=1x^0+42x^58+102x^60+6x^61+138x^62+12x^63+149x^64+62x^65+151x^66+154x^67+156x^68+224x^69+154x^70+338x^71+158x^72+428x^73+156x^74+372x^75+153x^76+246x^77+147x^78+128x^79+137x^80+54x^81+122x^82+18x^83+94x^84+4x^85+80x^86+2x^87+48x^88+24x^90+23x^92+9x^94+3x^96+1x^114
The gray image is a linear code over GF(2) with n=146, k=12 and d=58.
This code was found by Heurico 1.16 in 4.93 seconds.