The generator matrix

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

generates a code of length 9 over Z3[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+26x^15+66x^16+26x^18+84x^19+24x^21+12x^22+4x^24

The gray image is a linear code over GF(3) with n=27, k=5 and d=15.
This code was found by Heurico 1.16 in 0.000316 seconds.