The generator matrix

 1  0  0  0  1  1  1 2X^2+2X  1  1  1
 0  1  0  0 2X^2+2X 2X^2+1 2X+1  1 X^2+2X 2X^2+2X+1 X^2
 0  0  1  0 2X^2+2X+1 2X^2+1 2X+2 2X^2+X+1 2X^2+2X X+2  X
 0  0  0  1 2X^2+2X+2 2X^2+X X+2 2X^2+X+2 2X+1 X+1 X^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+78x^15+2124x^16+1464x^17+13480x^18+10098x^19+72612x^20+53498x^21+164970x^22+142632x^23+53532x^24+14238x^25+2478x^26+178x^27+54x^28+4x^30

The gray image is a linear code over GF(3) with n=99, k=12 and d=45.
This code was found by Heurico 1.16 in 45 seconds.