The generator matrix
1 0 1 1 1 X^2+X 1 1 X^2 1 1 X^2+X X^2 1 1 1 1 1 1 X^2+X
0 1 1 0 X^2+X+1 1 X X^2+X+1 1 0 X+1 1 1 X^2+1 X^2+X+1 0 X^2 X^2+1 X^2+1 1
0 0 X 0 X^2+X X^2 0 0 X^2+X X^2+X X X^2+X X^2 0 X^2 X X X X^2+X 0
0 0 0 X 0 X^2 X^2+X X X^2 X^2+X X X X^2+X X^2 X^2 X^2+X 0 X X X^2
0 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 0 0 X^2 0 0 0
generates a code of length 20 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.
Homogenous weight enumerator: w(x)=1x^0+125x^16+128x^17+254x^18+384x^19+284x^20+384x^21+246x^22+128x^23+90x^24+10x^26+12x^28+2x^30
The gray image is a linear code over GF(2) with n=80, k=11 and d=32.
This code was found by Heurico 1.16 in 0.0575 seconds.