The generator matrix

 1  0  0  0  1  1  1 2X  1  0  1
 0  1  0  0 2X  1 2X+1  1  0  1  X
 0  0  1  0 2X+1  1 2X+2 X+1  X 2X  0
 0  0  0  1 2X+2  X X+2 X+2  1  1 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+62x^15+138x^16+186x^17+412x^18+402x^19+576x^20+938x^21+774x^22+882x^23+1094x^24+582x^25+300x^26+160x^27+48x^28+4x^30+2x^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 0.062 seconds.