The generator matrix

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

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+28x^12+270x^14+58x^15+810x^16+432x^17+2488x^18+1620x^19+756x^20+80x^21+14x^24+4x^27

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 0.00775 seconds.