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.