The generator matrix

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

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+100x^14+8x^15+310x^16+104x^17+688x^18+400x^19+866x^20+400x^21+724x^22+104x^23+278x^24+8x^25+88x^26+14x^28+3x^32

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 0.205 seconds.