The generator matrix

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

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+126x^14+644x^15+1203x^16+2454x^17+3779x^18+4940x^19+6040x^20+5414x^21+4065x^22+2348x^23+1024x^24+514x^25+125x^26+68x^27+20x^28+2x^29+1x^30

The gray image is a linear code over GF(2) with n=80, k=15 and d=28.
This code was found by Heurico 1.13 in 2.56 seconds.