The generator matrix

1 0 0 0 0 0 1 1 1 X 0 0 0 0 1 1 1 X 0 X 1 1 1 1 1 0 1 1 1 1 1 0 1 1 X 0 X X X 0 X 1 X 0 1 X X 1 0 X 1 1 1 1 1 1 X 0 1 1 1 0
0 1 0 0 0 0 0 0 0 0 1 X 1 1 0 X+1 X X 1 1 1 0 X+1 X+1 X 0 1 X X+1 0 1 1 0 X X 1 1 1 1 0 1 1 0 1 X+1 0 1 X+1 1 1 1 X X 0 X+1 X+1 X 1 1 0 1 0
0 0 1 0 0 0 0 0 0 0 X 1 1 X+1 X+1 1 1 1 1 X 1 X+1 X 1 X+1 1 0 0 1 X+1 X 0 X X 1 0 X+1 0 0 1 1 X 1 1 1 0 X 1 0 1 X 1 1 1 X+1 X+1 1 0 X X+1 1 X
0 0 0 1 0 0 0 1 1 1 1 1 0 1 X 0 X+1 1 X 0 X 1 1 X+1 0 X X+1 1 X+1 X+1 X X X 0 X X X X X+1 X+1 1 0 0 X 0 1 1 X 1 X 0 X+1 X X X+1 1 1 0 1 0 1 0
0 0 0 0 1 0 1 0 X+1 1 1 1 X X+1 1 1 X X X+1 1 0 X+1 0 X+1 0 X+1 1 0 0 0 X X+1 X X+1 X X X+1 X 0 X 0 X+1 X+1 X X X+1 X+1 0 0 X X+1 0 1 1 1 X X+1 X+1 1 X 1 1
0 0 0 0 0 1 1 X+1 X 1 0 X 1 X+1 X X+1 0 X+1 0 X+1 0 1 0 X 1 X+1 X+1 1 X+1 X 1 1 0 1 0 X 0 X+1 1 1 1 X 1 1 1 X 1 0 1 X 1 X 0 1 1 X X+1 X 1 0 X+1 X+1
0 0 0 0 0 0 X X 0 0 0 0 0 0 X X X 0 0 0 X X X X X 0 0 0 0 0 0 X X 0 X X X X 0 X X 0 X X 0 X 0 0 X 0 X 0 0 X 0 0 X X 0 X 0 0

generates a code of length 62 over Z2[X]/(X^2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+64x^51+152x^52+248x^53+326x^54+368x^55+420x^56+392x^57+413x^58+472x^59+492x^60+490x^61+544x^62+522x^63+492x^64+506x^65+449x^66+418x^67+333x^68+318x^69+235x^70+174x^71+139x^72+86x^73+70x^74+30x^75+19x^76+8x^77+10x^78+1x^94

The gray image is a linear code over GF(2) with n=124, k=13 and d=51.
This code was found by Heurico 1.10 in 2.89 seconds.