The generator matrix

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

generates a code of length 15 over Z3[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+168x^28+120x^29+38x^30+336x^31+60x^32+2x^33+4x^36

The gray image is a linear code over GF(3) with n=135, k=6 and d=84.
This code was found by Heurico 1.16 in 0.000746 seconds.