The generator matrix

 1  0  0  1  1  1  1  1  1  1  1
 0  1  0  1  0  2  1  2  0  1  0
 0  0  1  2  1  2  1  0  2  1  0
 0  0  0 2X  0  0  X  0  X  X  0
 0  0  0  0 2X  0 2X  X 2X  X  0
 0  0  0  0  0  X 2X  0  X  X  X

generates a code of length 11 over Z3[X]/(X^2) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+36x^12+90x^14+192x^15+162x^16+720x^17+924x^18+972x^19+2646x^20+2412x^21+1944x^22+3852x^23+2442x^24+1296x^25+1440x^26+506x^27+36x^30+12x^33

The gray image is a linear code over GF(3) with n=33, k=9 and d=12.
This code was found by Heurico 1.16 in 0.161 seconds.