The generator matrix

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

generates a code of length 6 over Z3[X]/(X^2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+10x^9+60x^12+6x^15+4x^18

The gray image is a linear code over GF(3) with n=18, k=4 and d=9.
This code was found by Heurico 1.16 in 0.00011 seconds.