The generator matrix

X^2+X 1 1 1 1 X^2+X X^2+X X^2 1 1 1 X^2+X 0 1 1 0 1 0 1 1
1 0 X^2+X+1 1 X^2+X 1 X^2+X 0 X+1 1 X^2 1 1 0 X 1 X^2+X 1 X 0
0 0 X^2 X^2+1 X^2+X+1 1 1 1 X^2+X X+1 X^2+X X^2+X+1 0 1 1 1 0 X X X

generates a code of length 20 over Z2[X]/(X^3) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+24x^17+114x^18+96x^19+115x^20+40x^21+60x^22+16x^23+27x^24+16x^25+2x^26+1x^28

The gray image is a linear code over GF(2) with n=80, k=9 and d=34.
This code was found by an older version of Heurico in 0 seconds.