The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1 X^2  X  1 X^2  X  1  1  1
 0  X  0  0  0  0  0  0  0  X  X  X X^2 X^2+X  X  0  X X^2  X  0
 0  0  X  0  0  0  X X^2+X  X  X  X X^2+X  X X^2+X X^2  X  0 X^2  0  0
 0  0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2 X^2 X^2 X^2+X X^2+X X^2+X X^2  0
 0  0  0  0  X  X  0 X^2+X  X  0 X^2 X^2+X  X  X  X  0 X^2  X  X  0
 0  0  0  0  0 X^2  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 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+86x^12+88x^13+277x^14+332x^15+555x^16+930x^17+1759x^18+2722x^19+2806x^20+2754x^21+1812x^22+986x^23+564x^24+310x^25+232x^26+54x^27+84x^28+14x^29+15x^30+2x^31+1x^34

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 2.27 seconds.