The generator matrix

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

generates a code of length 62 over Z2[X]/(X^2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+19x^58+52x^59+38x^60+34x^61+25x^62+22x^63+21x^64+4x^65+14x^66+4x^67+2x^68+4x^69+2x^71+2x^72+3x^74+6x^77+3x^78

The gray image is a linear code over GF(2) with n=124, k=8 and d=58.
This code was found by Heurico 1.10 in 0.016 seconds.