The generator matrix

 1  0  1  1  1  1  1  0  1  1  1
 0  1  1  2  0 2X+1  2  1  0  0  X
 0  0 2X  0  0 2X 2X  X  0  X 2X
 0  0  0  X  0 2X  0 2X 2X 2X 2X
 0  0  0  0  X 2X  X 2X  X  X 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+54x^15+288x^18+870x^21+828x^24+134x^27+12x^30

The gray image is a linear code over GF(3) with n=33, k=7 and d=15.
This code was found by Heurico 1.16 in 0.00514 seconds.