The generator matrix

 1  1  1  1  1  1  1  1  X  1  X  1  1  1  X
 0  X 2X  0 2X^2+X 2X  0 2X^2+X 2X^2+X 2X^2+X 2X 2X^2+X  X 2X 2X^2+X
 0  0 X^2  0  0  0 X^2 2X^2 2X^2  0 2X^2  0 X^2 X^2 2X^2
 0  0  0 X^2  0 X^2 X^2 2X^2  0  0 2X^2 2X^2  0 2X^2 X^2
 0  0  0  0 2X^2 2X^2 X^2 2X^2 X^2 X^2 X^2  0  0 X^2 X^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+186x^24+162x^26+452x^27+486x^28+648x^29+2286x^30+972x^31+648x^32+630x^33+78x^36+12x^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 11.2 seconds.