The generator matrix

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

generates a code of length 6 over Z2[X]/(X^3) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+20x^5+21x^6+20x^7+1x^8+1x^10

The gray image is a linear code over GF(2) with n=24, k=6 and d=10.
As d=10 is an upper bound for linear (24,6,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 6.
This code was found by Heurico 1.16 in 6.82e-005 seconds.