The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1 X^2  1  1
 0  X  0 X^2+X  0 X^2+X X^2 X^2+X  0 X^2+X  0 X^2+X  0 X^2+X X^2 X^2  X X^2  0  0
 0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0
 0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0
 0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  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+21x^16+104x^18+25x^20+80x^22+10x^24+8x^26+6x^28+1x^36

The gray image is a linear code over GF(2) with n=80, k=8 and d=32.
This code was found by Heurico 1.16 in 0.00345 seconds.