The generator matrix

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

generates a code of length 3 over Z3[X]/(X^3) who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+72x^2+6x^3+1728x^4+288x^5+13836x^6+3456x^7+288x^8+8x^9

The gray image is a linear code over GF(3) with n=27, k=9 and d=6.
This code was found by Heurico 1.16 in 0.0041 seconds.