The generator matrix
1 1 1 1 1 1 1 1 1 X X
0 X 0 2X^2+X 0 X 2X 2X^2+2X 2X 2X^2 2X^2
0 0 X X^2+2X 2X X 0 2X^2+X 2X 2X^2+X 2X^2+X
0 0 0 X^2 0 2X^2 0 X^2 2X^2 2X^2 X^2
0 0 0 0 X^2 X^2 2X^2 X^2 X^2 2X^2 2X^2
generates a code of length 11 over Z3[X]/(X^3) who´s minimum homogenous weight is 15.
Homogenous weight enumerator: w(x)=1x^0+96x^15+162x^16+846x^18+972x^19+2664x^21+10692x^22+2694x^24+1296x^25+242x^27+18x^30
The gray image is a linear code over GF(3) with n=99, k=9 and d=45.
This code was found by Heurico 1.16 in 0.152 seconds.