The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X  0  0
 0  0 2X^2  0  0 X^2 2X^2 2X^2  0 2X^2  0
 0  0  0 X^2  0 2X^2 2X^2 X^2 2X^2  0  0
 0  0  0  0 2X^2 2X^2 X^2 2X^2 2X^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+42x^15+54x^16+318x^18+324x^19+3888x^20+852x^21+5022x^22+7776x^23+822x^24+432x^25+140x^27+12x^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 0.0886 seconds.