The generator matrix

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

generates a code of length 12 over Z3[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+96x^18+60x^19+414x^20+510x^21+3222x^22+1188x^23+5754x^24+6336x^25+1242x^26+668x^27+102x^28+72x^29+12x^30+6x^33

The gray image is a linear code over GF(3) with n=108, k=9 and d=54.
This code was found by Heurico 1.16 in 0.123 seconds.