The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1
 0  1  1  2  0  1  2  0  0  0  0  0
 0  0 2X  0  0  0  0  0  0  X  X  0
 0  0  0  X  0  0  0  0  X 2X 2X  0
 0  0  0  0  X  0  0  0 2X 2X  X  0
 0  0  0  0  0 2X  0  0 2X 2X 2X  0
 0  0  0  0  0  0  X  0 2X 2X  0  0
 0  0  0  0  0  0  0  X 2X  X  0  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+18x^10+152x^12+180x^13+356x^15+756x^16+728x^18+1800x^19+2916x^20+1172x^21+7254x^22+11664x^23+1466x^24+12204x^25+11664x^26+1288x^27+2880x^28+890x^30+1152x^31+392x^33+72x^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 0.719 seconds.