The generator matrix
1 0 1 1 1 1 1 0 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2
0 0 2X 0 0 0 0 X X X 2X
0 0 0 X 0 0 X X X 2X X
0 0 0 0 X 0 2X 0 X X X
0 0 0 0 0 2X X 2X X 0 2X
generates a code of length 11 over Z3[X]/(X^2) who´s minimum homogenous weight is 15.
Homogenous weight enumerator: w(x)=1x^0+132x^15+162x^16+294x^18+972x^19+648x^21+1944x^22+978x^24+1296x^25+110x^27+24x^33
The gray image is a linear code over GF(3) with n=33, k=8 and d=15.
This code was found by Heurico 1.16 in 0.607 seconds.