The generator matrix

 1  0  0  0  0  1
 0  1  0  0  0  X
 0  0  1  0  0  X
 0  0  0  1  0  X
 0  0  0  0  1  X

generates a code of length 6 over Z2[X]/(X^3) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+114x^2+512x^3+2735x^4+7168x^5+11708x^6+7168x^7+2735x^8+512x^9+114x^10+1x^12

The gray image is a linear code over GF(2) with n=24, k=15 and d=4.
As d=4 is an upper bound for linear (24,15,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 15.
This code was found by Heurico 1.13 in 3.81e-009 seconds.