The generator matrix

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

generates a code of length 16 over Z3[X]/(X^3) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+152x^30+144x^31+54x^32+300x^33+72x^34+2x^36+4x^39

The gray image is a linear code over GF(3) with n=144, k=6 and d=90.
This code was found by Heurico 1.16 in 0.000846 seconds.