The generator matrix

 1  0  1  1  1 X^2+X  1 X^2  1  0  1  1  1  1 X^2+X  1  X  1  1  X
 0  1  1  0 X^2+X+1  1  X  1 X+1  1 X^2+1  X X^2+X X^2+X+1  1 X^2+1 X^2  1  1 X^2
 0  0  X  0 X^2+X  0  0 X^2  X  X  0 X^2+X  0 X^2 X^2+X X^2  X  X  X  0
 0  0  0  X  0  0 X^2+X X^2+X  X  X X^2 X^2 X^2 X^2+X  X  0  0 X^2 X^2+X  X
 0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2
 0  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 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+94x^15+184x^16+392x^17+280x^18+782x^19+626x^20+816x^21+272x^22+394x^23+142x^24+72x^25+24x^26+10x^27+6x^28+1x^32

The gray image is a linear code over GF(2) with n=80, k=12 and d=30.
This code was found by Heurico 1.16 in 10.1 seconds.