The generator matrix

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

generates a code of length 12 over Z3[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+162x^15+1026x^18+3954x^21+8688x^24+5246x^27+582x^30+6x^33+18x^36

The gray image is a linear code over GF(3) with n=36, k=9 and d=15.
This code was found by Heurico 1.16 in 0.288 seconds.