The generator matrix

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

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+58x^18+64x^19+59x^20+16x^21+24x^22+16x^23+11x^24+6x^26+1x^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 0.00259 seconds.