The generator matrix

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

generates a code of length 12 over Z3[X]/(X^3) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+6x^21+90x^22+552x^24+36x^25+6x^27+36x^28+2x^36

The gray image is a linear code over GF(3) with n=108, k=6 and d=63.
This code was found by Heurico 1.16 in 0.000942 seconds.