The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  1  X  1  X  X
 0  X  0  0  0  X X^2+X  X  0 X^2  0 X^2  X X^2+X X^2 X^2+X  X  X X^2+X X^2
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X  0  X X^2 X^2+X  X X^2  X X^2+X  X
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  0  X X^2  0 X^2+X  0 X^2+X  X  X X^2
 0  0  0  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  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 14.

Homogenous weight enumerator: w(x)=1x^0+53x^14+150x^15+218x^16+324x^17+326x^18+546x^19+849x^20+536x^21+347x^22+378x^23+201x^24+100x^25+37x^26+14x^27+11x^28+4x^30+1x^34

The gray image is a linear code over GF(2) with n=80, k=12 and d=28.
This code was found by Heurico 1.16 in 0.209 seconds.