The generator matrix

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

generates a code of length 69 over Z2[X]/(X^2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+29x^62+88x^63+102x^64+96x^65+100x^66+88x^67+67x^68+72x^69+60x^70+50x^71+41x^72+30x^73+35x^74+22x^75+24x^76+22x^77+21x^78+14x^79+12x^80+12x^81+7x^82+10x^83+7x^84+6x^85+4x^86+2x^88+2x^89

The gray image is a linear code over GF(2) with n=138, k=10 and d=62.
This code was found by Heurico 1.10 in 0.063 seconds.