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.