The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  X X^2 X^2 X^2+X X^2+X  0  0 X^2  0 X^2+X  X  0  0
 0  0  X  0  0  0  0  X  0 X^2+X X^2+X X^2 X^2  0  X  X  X X^2+X X^2  0
 0  0  0  X  0  0  0  X  X X^2  X  0 X^2  X  X  0 X^2 X^2  0  0
 0  0  0  0  X  0  X  X  X X^2+X X^2  X  0  X  0 X^2 X^2 X^2+X X^2+X  0
 0  0  0  0  0  X  X X^2  X  X  X X^2+X  0 X^2  X  X  0  0 X^2+X X^2
 0  0  0  0  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0 X^2  0 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+45x^12+108x^13+206x^14+348x^15+415x^16+612x^17+786x^18+980x^19+9382x^20+980x^21+786x^22+612x^23+415x^24+348x^25+206x^26+108x^27+45x^28+1x^40

The gray image is a linear code over GF(2) with n=80, k=14 and d=24.
This code was found by Heurico 1.16 in 2.54 seconds.