The generator matrix
1 0 1 1 1 X^2+X 1 X^2 1 1 X 1 0 1 1 1 X^2+X 1 1 1
0 1 1 X^2+X X^2+X+1 1 X^2 1 X+1 X 1 X^2+1 1 X X^2 X^2+1 1 X+1 X X^2
0 0 X 0 X^2+X X^2 X X 0 X^2+X X^2+X 0 X^2 X X X^2 X^2 0 X X^2+X
0 0 0 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0 X^2 X^2 X^2
0 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2 X^2 0 X^2 0 X^2 0 X^2 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+50x^16+64x^17+136x^18+192x^19+157x^20+192x^21+112x^22+64x^23+41x^24+8x^26+7x^28
The gray image is a linear code over GF(2) with n=80, k=10 and d=32.
This code was found by Heurico 1.16 in 0.0139 seconds.