The generator matrix

 1  0  1  1  1  1  1 2X^2+X  1  1  1  1  1  1  1
 0  1 2X^2+2X+1  2 2X^2+X X+1 2X^2+X+2  1 2X 2X+2 2X^2+1 X+1 2X^2+2X+1 2X^2+X+2  0
 0  0 2X^2  0 2X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0
 0  0  0 X^2 2X^2 2X^2 X^2  0 X^2 2X^2  0 X^2  0 2X^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+14x^24+36x^25+282x^26+20x^27+1224x^28+972x^29+498x^30+2412x^31+990x^32+20x^33+54x^34+24x^35+6x^36+6x^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 0.0209 seconds.