The generator matrix

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

generates a code of length 68 over Z2[X]/(X^2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+72x^58+120x^59+158x^60+212x^61+256x^62+262x^63+235x^64+250x^65+232x^66+236x^67+236x^68+232x^69+207x^70+210x^71+176x^72+196x^73+187x^74+134x^75+152x^76+100x^77+79x^78+48x^79+32x^80+34x^81+21x^82+14x^83+2x^84+2x^86

The gray image is a linear code over GF(2) with n=136, k=12 and d=58.
This code was found by Heurico 1.10 in 0.86 seconds.