The generator matrix

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

generates a code of length 15 over Z3[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+54x^24+132x^25+144x^26+186x^27+762x^28+108x^29+3148x^30+1350x^31+162x^32+214x^33+156x^34+72x^35+38x^36+30x^37+2x^39+2x^42

The gray image is a linear code over GF(3) with n=135, k=8 and d=72.
This code was found by Heurico 1.16 in 0.0366 seconds.