The generator matrix

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

generates a code of length 12 over Z3[X]/(X^3) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+126x^17+2628x^18+1866x^19+14070x^20+13056x^21+71676x^22+55368x^23+154884x^24+140706x^25+55530x^26+18170x^27+2994x^28+294x^29+66x^30+6x^33

The gray image is a linear code over GF(3) with n=108, k=12 and d=51.
This code was found by Heurico 1.16 in 55.1 seconds.