The generator matrix

 1  0  0  0  1  1  1 X^2+X  1 X^2+X  0  1  1  X X^2  1  0  1  1  1
 0  1  0  0  0  1 X^2+X+1  1 X^2 X^2  1 X^2  1  1  X X^2  1 X^2+X  0 X^2+X
 0  0  1  0  1  1  X X+1 X^2+X  1 X^2+X+1 X+1  0  X X^2 X^2+X+1 X^2+X+1 X^2+X+1  X  0
 0  0  0  1  1  0 X^2  0  1 X^2+X+1 X^2+1 X^2+X X^2+1  1  1 X^2+X  X X^2+1  1 X^2+X
 0  0  0  0  X  0  0 X^2  0 X^2 X^2+X X^2+X X^2 X^2+X  X X^2  0  0 X^2+X  X
 0  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2  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+171x^14+522x^15+1413x^16+2128x^17+3985x^18+4914x^19+6223x^20+5232x^21+4111x^22+2126x^23+1309x^24+384x^25+179x^26+54x^27+13x^28+2x^30+1x^32

The gray image is a linear code over GF(2) with n=80, k=15 and d=28.
This code was found by Heurico 1.16 in 6.96 seconds.