The generator matrix

 1  0  1  1  1  0  1  1  0  1 X^2  1  1 X^2 X^2  1  1 X^2+X  1  1
 0  1  1  0  1  1  0 X+1  1 X^2  1 X+1  0  1  X X^2+X+1 X^2  1 X+1 X^2
 0  0  X  0  0  0  0  0  0 X^2 X^2  X  X  X X^2 X^2+X  X X^2 X^2  X
 0  0  0  X  0  0 X^2+X X^2 X^2+X  0  X  X  X  X X^2+X  X X^2+X X^2+X X^2+X  0
 0  0  0  0  X X^2+X X^2+X X^2  X  X  0 X^2  0  X  0 X^2+X  X  X X^2+X X^2
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  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+60x^14+158x^15+282x^16+592x^17+919x^18+1320x^19+1583x^20+1258x^21+896x^22+622x^23+301x^24+132x^25+44x^26+12x^27+9x^28+2x^29+1x^34

The gray image is a linear code over GF(2) with n=80, k=13 and d=28.
This code was found by Heurico 1.16 in 0.709 seconds.