The generator matrix

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

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+205x^16+400x^17+532x^18+576x^19+717x^20+560x^21+524x^22+352x^23+168x^24+32x^25+24x^26+5x^28

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 0.137 seconds.