The generator matrix

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

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+498x^18+1458x^20+1668x^21+7290x^22+5832x^23+19422x^24+14580x^25+5832x^26+2264x^27+204x^30

The gray image is a linear code over GF(3) with n=108, k=10 and d=54.
This code was found by Heurico 1.16 in 0.997 seconds.