The generator matrix

 1  0  1  1  1 X^2  1  0  1  1 X^2  1  1  1  1  1  1  1  1  1
 0  1  1  0  1  1 X^2  1  0 X+1  1 X^2+1  0  0 X^2+X+1 X^2+X+1  X  1 X^2+X+1 X^2+X
 0  0  X  0  0  0  0  0  0 X^2 X^2 X^2+X  X X^2+X X^2+X X^2 X^2+X X^2  X X^2+X
 0  0  0  X  0  0 X^2 X^2+X X^2+X  0 X^2+X X^2 X^2 X^2+X  0 X^2+X X^2  X  0 X^2+X
 0  0  0  0  X X^2+X X^2+X  X X^2+X  0 X^2  X X^2+X X^2+X X^2  0 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 16.

Homogenous weight enumerator: w(x)=1x^0+414x^16+768x^18+1744x^20+768x^22+384x^24+16x^28+1x^32

The gray image is a linear code over GF(2) with n=80, k=12 and d=32.
This code was found by Heurico 1.16 in 16.3 seconds.