The generator matrix

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

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+612x^15+2508x^18+7704x^21+7434x^24+1406x^27+18x^30

The gray image is a linear code over GF(3) with n=33, k=9 and d=15.
This code was found by Heurico 1.16 in 58.4 seconds.