The generator matrix
1 0 1 1 1 X^2+X 1 1 0 1 1 X^2+X 1 1 1 1 1 1 0 X^2
0 1 X+1 X^2+X X^2+1 1 0 X+1 1 X^2+X X^2+1 1 X^2 X^2+X X X+1 X^2+X+1 0 1 1
0 0 X^2 0 X^2 0 0 X^2 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 X^2
0 0 0 X^2 X^2 X^2 X^2 X^2 X^2 0 0 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 18.
Homogenous weight enumerator: w(x)=1x^0+89x^18+76x^20+86x^22+1x^24+1x^26+2x^28
The gray image is a linear code over GF(2) with n=80, k=8 and d=36.
As d=37 is an upper bound for linear (80,8,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 8.
This code was found by Heurico 1.16 in 0.00372 seconds.