The generator matrix

 1  0  1  1  1  1  1  1  1  X  1
 0  1  1  2 2X+1 2X^2 2X^2+X 2X^2+2X+1 2X^2+X  X X+1
 0  0 2X  0  X 2X^2+X 2X^2+2X 2X^2 2X^2  X  0
 0  0  0 X^2  0 2X^2 2X^2 2X^2 X^2 2X^2  0
 0  0  0  0 X^2 2X^2  0 2X^2 X^2  0 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+88x^15+378x^16+2060x^18+1908x^19+5346x^20+7970x^21+19872x^22+10692x^23+7920x^24+2592x^25+162x^27+36x^28+22x^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 0.722 seconds.