The generator matrix

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

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+1026x^18+432x^19+4860x^20+4956x^21+21546x^22+19440x^23+54990x^24+43092x^25+19440x^26+6632x^27+540x^28+192x^30

The gray image is a linear code over GF(3) with n=108, k=11 and d=54.
This code was found by Heurico 1.16 in 6.7 seconds.