The generator matrix

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

generates a code of length 12 over Z3[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+6x^21+66x^24+6x^27+2x^36

The gray image is a linear code over GF(3) with n=36, k=4 and d=21.
This code was found by Heurico 1.16 in 0.000324 seconds.