The generator matrix

 1  0  0  1  1  1  1  1  1
 0  1  0 2X^2+2X  1 2X^2+X 2X^2+2X+2  X 2X^2+2X+1
 0  0  1 2X^2+2X+1  1 2X^2+2X+2 2X^2+2X+1  1 2X^2+2X+2
 0  0  0 2X^2 X^2  0 X^2 2X^2 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+116x^12+1476x^14+722x^15+7614x^16+5508x^17+21788x^18+15228x^19+5616x^20+928x^21+36x^23+16x^24

The gray image is a linear code over GF(3) with n=81, k=10 and d=36.
This code was found by Heurico 1.16 in 0.427 seconds.