The generator matrix

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

generates a code of length 9 over Z3[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+62x^12+234x^14+128x^15+648x^16+864x^17+2240x^18+1296x^19+810x^20+226x^21+36x^23+16x^24

The gray image is a linear code over GF(3) with n=81, k=8 and d=36.
This code was found by Heurico 1.16 in 0.0136 seconds.