The generator matrix

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

generates a code of length 20 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+24x^12+8x^13+54x^14+56x^15+121x^16+424x^17+208x^18+1048x^19+208x^20+1048x^21+201x^22+424x^23+142x^24+56x^25+40x^26+8x^27+16x^28+8x^30+1x^38

The gray image is a linear code over GF(2) with n=80, k=12 and d=24.
This code was found by Heurico 1.16 in 0.131 seconds.