The generator matrix
1 0 1 1 1 1 1 1 1 1 1
0 1 1 2 0 1 2 0 0 0 0
0 0 2X 0 0 0 0 X 0 X 0
0 0 0 X 0 0 0 2X X 2X 0
0 0 0 0 X 0 0 2X 2X X 0
0 0 0 0 0 2X 0 2X 2X 2X 0
0 0 0 0 0 0 X 2X X X 0
generates a code of length 11 over Z3[X]/(X^2) who´s minimum homogenous weight is 9.
Homogenous weight enumerator: w(x)=1x^0+30x^9+18x^10+98x^12+144x^13+190x^15+468x^16+1302x^18+864x^19+1458x^20+4382x^21+1152x^22+2916x^23+4360x^24+1152x^25+368x^27+576x^28+164x^30+40x^33
The gray image is a linear code over GF(3) with n=33, k=9 and d=9.
This code was found by Heurico 1.16 in 0.0883 seconds.