The generator matrix

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

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+72x^6+168x^9+756x^12+1260x^15+14970x^18+1512x^21+774x^24+170x^27

The gray image is a linear code over GF(3) with n=27, k=9 and d=6.
This code was found by Heurico 1.16 in 0.119 seconds.