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.