The generator matrix

 1  0  0  0  1  1
 0  1  0  0  1  X
 0  0  1  0  1 X+1
 0  0  0  1  X  1

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

Homogenous weight enumerator: w(x)=1x^0+96x^3+279x^4+1056x^5+1232x^6+1056x^7+279x^8+96x^9+1x^12

The gray image is a linear code over GF(2) with n=24, k=12 and d=6.
This code was found by Heurico 1.11 in 3.81e-009 seconds.