The generator matrix

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

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+130x^17+149x^18+210x^19+106x^20+184x^21+102x^22+88x^23+21x^24+22x^25+5x^26+6x^27

The gray image is a linear code over GF(2) with n=80, k=10 and d=34.
This code was found by Heurico 1.11 in 0.157 seconds.