The generator matrix

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

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+54x^4+148x^6+49x^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 0.000216 seconds.