The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+30x^9+84x^12+138x^15+1650x^18+186x^21+78x^24+20x^27

The gray image is a linear code over GF(3) with n=27, k=7 and d=9.
This code was found by Heurico 1.16 in 0.00305 seconds.