The generator matrix

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

generates a code of length 20 over Z2[X]/(X^3) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+170x^13+762x^14+2138x^15+4606x^16+9096x^17+15333x^18+21410x^19+24077x^20+21108x^21+15465x^22+9534x^23+4549x^24+1864x^25+695x^26+198x^27+47x^28+18x^29+1x^30

The gray image is a linear code over GF(2) with n=80, k=17 and d=26.
This code was found by Heurico 1.13 in 32 seconds.