The generator matrix

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

generates a code of length 9 over Z3[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+36x^12+72x^15+510x^18+72x^21+36x^24+2x^27

The gray image is a linear code over GF(3) with n=27, k=6 and d=12.
This code was found by Heurico 1.16 in 0.000717 seconds.