The generator matrix
1 0 0 1 1 1 1 1 1 1 1
0 1 0 1 0 2 1 2 0 2X+1 0
0 0 1 2 1 2 1 0 0 2X+2 0
0 0 0 2X 0 0 0 X 0 2X 0
0 0 0 0 2X 0 0 2X 0 2X 0
0 0 0 0 0 X 0 2X X 2X 0
0 0 0 0 0 0 X X 2X 0 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+32x^9+306x^12+162x^14+1492x^15+324x^16+1296x^17+4832x^18+1944x^19+3888x^20+10596x^21+8262x^22+5184x^23+11536x^24+2592x^25+2592x^26+3802x^27+168x^30+40x^33
The gray image is a linear code over GF(3) with n=33, k=10 and d=9.
This code was found by Heurico 1.16 in 0.636 seconds.