The generator matrix

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

generates a code of length 81 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+245x^68+662x^70+1005x^72+1324x^74+1445x^76+1668x^78+1848x^80+1808x^82+1812x^84+1544x^86+1209x^88+892x^90+501x^92+252x^94+113x^96+40x^98+12x^100+2x^102+1x^132

The gray image is a linear code over GF(2) with n=162, k=14 and d=68.
This code was found by Heurico 1.10 in 15.3 seconds.