The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+18x^2+6x^3+108x^4+72x^5+228x^6+216x^7+72x^8+8x^9

The gray image is a linear code over GF(3) with n=9, k=6 and d=2.
This code was found by Heurico 1.16 in 3.7e-005 seconds.