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 X X 1 1 1 X 1 1 1 1 1 1 X X 1 1 X 1 X X 1 1 1 X 1 X 0 0 0 0 1 1
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 X X 0 X 0 0 0 X 0 X 0 0 0 X 0 0 0 X X X X X 0 0 X 0 X X X X 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 0 X X X 0 X 0 X X X 0 0 X 0 X X X X 0 0 0 0 X 0 0 0 0 X X X 0 0
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 X X 0 X X X X 0 0 X 0 0 0 0 X X 0 X 0 X X 0 X 0 0 0 X X 0 0 X 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 X 0 0 X 0 X X 0 X 0 0 0 X 0 0 X 0 0 0 0 X X 0 X X X X X 0 0 X 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 0 X X X X 0 X X 0 X 0 X 0 0 0 X X 0 0 X X X X X 0 X 0 X X 0 X X
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 0 X X X 0 0 X 0 X X 0 X 0 0 X 0 X 0 0 X X 0 X 0 0 X 0 0 X 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 0 X X 0 X 0 X X 0 X 0 X 0 X X 0 X 0 0 X 0 X X 0 0 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 0 0 X X 0 X 0 0 0 0 X 0 0 X X X X X 0 X X X X 0 X X 0 X X 0 X 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+64x^52+20x^54+156x^56+56x^58+189x^60+96x^62+180x^64+72x^66+87x^68+12x^70+52x^72+27x^76+10x^80+1x^84+1x^96
The gray image is a linear code over GF(2) with n=124, k=10 and d=52.
This code was found by Heurico 1.16 in 0.255 seconds.