The generator matrix

 1  0  1  1  1  1  1 2X^2  1  1  1
 0  1  1  2  0 2X+1 2X^2+2  1 2X^2+2X X+1 2X^2
 0  0 2X  0 X^2  X 2X^2+X X^2+X X^2+X 2X^2  X
 0  0  0  X 2X^2+2X 2X^2 X^2+2X 2X 2X^2+2X X^2+2X 2X^2+2X

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+210x^16+216x^17+1482x^18+702x^19+8316x^20+5584x^21+18936x^22+16416x^23+5616x^24+978x^25+324x^26+134x^27+72x^28+2x^30+2x^33

The gray image is a linear code over GF(3) with n=99, k=10 and d=45.
This code was found by Heurico 1.16 in 0.804 seconds.