The generator matrix

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

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+72x^12+190x^14+474x^16+256x^17+804x^18+1792x^19+964x^20+1792x^21+896x^22+256x^23+460x^24+156x^26+68x^28+2x^30+9x^32

The gray image is a linear code over GF(2) with n=80, k=13 and d=24.
This code was found by Heurico 1.16 in 0.619 seconds.