The generator matrix

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

generates a code of length 19 over Z2[X]/(X^3) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+58x^17+57x^18+66x^19+22x^20+14x^21+14x^22+22x^23+1x^24+1x^26

The gray image is a linear code over GF(2) with n=76, k=8 and d=34.
As d=35 is an upper bound for linear (76,8,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 8.
This code was found by Heurico 1.16 in 0.0407 seconds.