The generator matrix

 1  0  1  1  1  1
 0  1 X+1 X^2+X  0 X^2+X
 0  0 X^2  0 X^2  0
 0  0  0 X^2 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+26x^4+48x^5+108x^6+48x^7+21x^8+4x^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 0.00019 seconds.