The generator matrix
1 0 0 1 1 1 0 1 1 1 1 1 0 X 0 1 0 1 X 1 X 1 1 1 0 1 1 X 1 X 0 1 X 1 1 1 1 X X 1 1 1 1 X 1 1 0 1 1 X 0 0 1 X X 1 1 X 1 X 1 0
0 1 0 1 0 1 1 0 0 1 X+1 X 1 1 0 X 0 X+1 1 X+1 1 1 0 1 X X 0 1 0 1 1 1 1 X X 1 1 0 1 0 0 X X+1 1 1 X 0 X+1 X+1 0 1 1 0 1 1 1 X 1 X 1 1 1
0 0 1 1 1 0 1 0 1 X+1 X 1 X 1 1 0 1 X+1 X X 1 1 0 1 1 0 X X+1 1 0 1 0 X+1 X+1 1 1 X+1 1 1 1 0 0 X X+1 1 X 1 X 1 1 X 0 X+1 0 X X+1 0 1 X+1 X X+1 0
0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 0 X 0 0 0 X 0 X 0 0 0 X 0 0 X 0 X X X X X 0 X X X X 0 0 X X X X 0 0 X X X 0 X X X 0 0 0 X X
0 0 0 0 X 0 0 0 0 0 0 0 X X X X 0 X 0 0 X 0 0 X X 0 X 0 X X 0 0 X X X 0 0 0 X X X 0 X 0 X 0 0 X 0 0 0 X 0 X 0 0 X X 0 0 X 0
0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 0 X X X X X X X X 0 X X X X X X X 0 X 0 0 0 0 X 0 X X 0 0 X 0 X 0 0 X X 0 X X X X X 0 0
0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X X X X 0 X X X 0 X X 0 X X X 0 X 0 0 X X X X X X X 0 X X 0 0 0 X X X 0 0 X X X X X 0 0 X
0 0 0 0 0 0 0 X 0 X X X 0 0 X 0 X X 0 X 0 X 0 0 X X X 0 0 X X 0 0 X X X 0 0 X X 0 X X 0 0 0 0 X 0 X X 0 0 0 X X 0 0 X 0 0 X
0 0 0 0 0 0 0 0 X 0 0 X X X X X 0 X 0 0 0 X X 0 0 X 0 0 X 0 X 0 0 X X X 0 X 0 X 0 0 X 0 X X X 0 0 0 0 X X 0 X 0 0 X X X 0 X
generates a code of length 62 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.
Homogenous weight enumerator: w(x)=1x^0+148x^52+228x^54+493x^56+422x^58+594x^60+452x^62+522x^64+472x^66+339x^68+184x^70+156x^72+34x^74+36x^76+11x^80+3x^84+1x^88
The gray image is a linear code over GF(2) with n=124, k=12 and d=52.
This code was found by Heurico 1.16 in 2.51 seconds.