The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1  0  1  1  1  1  1  1  X  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X+1  1  0 X^2+X X^2 X^2+X  X  0 X^2+X  0
 0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0
 0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0
 0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  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+23x^16+40x^17+65x^18+88x^19+84x^20+88x^21+58x^22+40x^23+20x^24+2x^26+2x^30+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 0.00502 seconds.