The generator matrix

 1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0 2X^2  X 2X^2+X  X 2X^2 2X^2+2X  0
 0  0  X  0 2X^2+X 2X 2X X^2 2X  X  0
 0  0  0  X 2X^2+2X X^2+X X^2+2X 2X^2+X 2X^2  X 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+58x^15+174x^16+156x^17+338x^18+594x^19+396x^20+752x^21+14400x^22+684x^23+894x^24+798x^25+222x^26+138x^27+72x^28+4x^30+2x^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 0.165 seconds.