The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^2  X  0
 0  X  0  X  0  0 X^2+X X^2+X X^2 X^2+X X^2  X  X  0 X^2  X  X  X X^2+X  X
 0  0  X  X  0 X^2+X  X X^2 X^2 X^2  X X^2  X X^2  X X^2+X X^2+X  X  0 X^2
 0  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2

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+90x^18+92x^20+60x^22+2x^24+10x^26+1x^32

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 0.297 seconds.