The generator matrix

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

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+50x^24+48x^26+84x^27+216x^28+36x^29+1100x^30+432x^31+54x^32+98x^33+24x^35+38x^36+4x^39+2x^42

The gray image is a linear code over GF(3) with n=135, k=7 and d=72.
This code was found by Heurico 1.16 in 0.00556 seconds.