The generator matrix

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

generates a code of length 20 over Z2[X]/(X^3) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+124x^15+377x^16+640x^17+950x^18+1268x^19+1432x^20+1344x^21+998x^22+580x^23+302x^24+128x^25+34x^26+12x^27+2x^30

The gray image is a linear code over GF(2) with n=80, k=13 and d=30.
This code was found by Heurico 1.16 in 0.537 seconds.