The generator matrix

 1  0  0  1  1  1  1  1  1
 0  1  0  1  0  2  1  2  0
 0  0  1  2  1  2  1  0  0
 0  0  0 2X  0  0  X  0  X
 0  0  0  0 2X  0 2X  X 2X
 0  0  0  0  0  X 2X  0  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+54x^10+408x^12+432x^13+486x^14+2082x^15+1296x^16+1944x^17+5538x^18+1728x^19+1944x^20+2778x^21+864x^22+78x^24+20x^27

The gray image is a linear code over GF(3) with n=27, k=9 and d=9.
This code was found by Heurico 1.16 in 0.113 seconds.