The generator matrix

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

generates a code of length 20 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+18x^16+46x^17+58x^18+86x^19+110x^20+88x^21+46x^22+24x^23+15x^24+10x^25+7x^26+2x^27+1x^34

The gray image is a linear code over GF(2) with n=80, k=9 and d=32.
This code was found by Heurico 1.16 in 0.00621 seconds.