The generator matrix

 1  0  0  1  1  1  0 X^2  1 X^2+X  1  1  X  1  1 X^2+X  1 X^2 X^2  1
 0  1  0  0 X^2+1 X^2+1  1  X X^2  1  X X^2+X+1  1 X+1  0  X  X  1  1 X^2+1
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1  X  0 X^2+X+1  1 X^2+1 X^2  X  1 X^2+X X^2+X+1 X^2+1 X+1
 0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 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+122x^17+153x^18+214x^19+110x^20+204x^21+82x^22+68x^23+33x^24+26x^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 1.16 in 0.134 seconds.