The generator matrix

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

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+16x^3+39x^4+48x^5+304x^6+48x^7+39x^8+16x^9+1x^12

The gray image is a linear code over GF(2) with n=24, k=9 and d=6.
This code was found by Heurico 1.16 in 0.000292 seconds.