The generator matrix

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

generates a code of length 6 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+21x^4+66x^5+85x^6+60x^7+18x^8+2x^9+3x^10

The gray image is a linear code over GF(2) with n=24, k=8 and d=8.
As d=8 is an upper bound for linear (24,8,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 8.
This code was found by Heurico 1.16 in 0.000185 seconds.