The generator matrix

 1  0  1  1  1  1  1  1  1
 0  1  1  2  0  1  2  0  0
 0  0 2X  0  0  0  X  0  X
 0  0  0  X  0  0 2X  0  X
 0  0  0  0  X  0  X  X  0
 0  0  0  0  0 2X 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+32x^9+18x^10+78x^12+144x^13+324x^14+138x^15+918x^16+1296x^17+212x^18+1548x^19+1296x^20+156x^21+288x^22+96x^24+16x^27

The gray image is a linear code over GF(3) with n=27, k=8 and d=9.
This code was found by Heurico 1.16 in 0.00938 seconds.