The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+42x^6+84x^9+252x^12+420x^15+4878x^18+504x^21+294x^24+86x^27

The gray image is a linear code over GF(3) with n=27, k=8 and d=6.
This code was found by Heurico 1.16 in 0.00952 seconds.