The generator matrix

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

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+18x^21+198x^24+26x^27

The gray image is a linear code over GF(3) with n=108, k=5 and d=63.
This code was found by Heurico 1.16 in 0.000383 seconds.