The generator matrix

 1  0  0  1  1  1  X  X  1  1  1  1 X^2+X  1  1  1  1 X^2+X  1  1
 0  1  0  0  1  1  1  1 X+1  X X^2 X^2  0  X  X X^2 X+1  1 X^2+X X^2
 0  0  1 X+1 X^2+X+1  0  1  X X^2+X+1  1 X^2+1  X  1 X^2+X+1  1 X+1  0 X+1 X+1  1
 0  0  0 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0
 0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 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+330x^16+128x^17+712x^18+384x^19+1012x^20+384x^21+688x^22+128x^23+308x^24+8x^26+12x^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 34 seconds.