The generator matrix

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

generates a code of length 15 over Z3[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+474x^26+238x^27+270x^28+1620x^29+1558x^30+540x^31+1548x^32+210x^33+84x^35+16x^36+2x^39

The gray image is a linear code over GF(3) with n=135, k=8 and d=78.
This code was found by Heurico 1.16 in 0.041 seconds.