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.