The generator matrix

 1  1  1  1  1  1  X  X  0  1  1
 0  X 2X  0 2X^2+X 2X 2X^2+X 2X  X  0 2X^2+X
 0  0 X^2  0  0  0 2X^2  0 X^2 2X^2 2X^2
 0  0  0 X^2  0  0 2X^2 X^2 X^2 X^2 X^2
 0  0  0  0 2X^2  0 2X^2 X^2 2X^2 2X^2  0
 0  0  0  0  0 X^2  0 2X^2 X^2 2X^2 X^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+132x^15+162x^16+294x^18+972x^19+4374x^20+648x^21+1944x^22+8748x^23+978x^24+1296x^25+110x^27+24x^33

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 3.03 seconds.