The generator matrix

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

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+786x^24+216x^25+1458x^26+2360x^27+7128x^28+5832x^29+17298x^30+14256x^31+5832x^32+3282x^33+270x^34+330x^36

The gray image is a linear code over GF(3) with n=135, k=10 and d=72.
This code was found by Heurico 1.16 in 1.46 seconds.