The generator matrix

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

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+80x^9+324x^12+864x^15+2184x^18+3888x^21+43956x^24+4136x^27+2592x^30+864x^33+160x^36

The gray image is a linear code over GF(3) with n=36, k=10 and d=9.
This code was found by Heurico 1.16 in 1.3 seconds.