The generator matrix

 1  0  1  1  1  0  1  1  X  1  1 X^2 X^2+X  X  X  1  1  X X^2+X  1
 0  1  1  0 X+1  1  X X^2+X+1  1 X^2+X X^2+1  1  1  1  1  0 X^2+X X^2  1  0
 0  0  X X^2+X  0 X^2+X  X  X X^2+X  0 X^2 X^2+X  0  X X^2+X X^2  0  X X^2  0
 0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0
 0  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  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+30x^14+70x^15+114x^16+380x^17+352x^18+826x^19+544x^20+840x^21+360x^22+378x^23+100x^24+60x^25+24x^26+6x^27+8x^28+2x^30+1x^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 0.136 seconds.