The generator matrix

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

generates a code of length 12 over Z3[X]/(X^3) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+42x^19+696x^20+634x^21+2310x^22+2508x^23+5610x^24+4542x^25+2616x^26+638x^27+72x^28+12x^29+2x^30

The gray image is a linear code over GF(3) with n=108, k=9 and d=57.
This code was found by Heurico 1.16 in 0.102 seconds.