The generator matrix

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

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+35x^16+40x^17+63x^18+24x^19+180x^20+40x^21+84x^22+8x^23+8x^24+16x^25+12x^26+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 0.00682 seconds.