The generator matrix

 1  0  1  1  1  1  1  1  1
 0  1  1  2  0  0  0  0  0
 0  0 2X  0  0  0  0  0  X
 0  0  0  X  0  0  0  0  X
 0  0  0  0  X  0  0  0  X
 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+90x^6+384x^9+1836x^12+4140x^15+13122x^16+6168x^18+26244x^19+4968x^21+1926x^24+170x^27

The gray image is a linear code over GF(3) with n=27, k=10 and d=6.
This code was found by Heurico 1.16 in 0.477 seconds.