The generator matrix

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

generates a code of length 12 over Z3[X]/(X^2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+44x^9+152x^12+356x^15+728x^18+1172x^21+14588x^24+1288x^27+890x^30+392x^33+72x^36

The gray image is a linear code over GF(3) with n=36, k=9 and d=9.
This code was found by Heurico 1.16 in 0.157 seconds.