The generator matrix

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

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+62x^30+54x^32+120x^33+2x^36+4x^39

The gray image is a linear code over GF(3) with n=144, k=5 and d=90.
This code was found by Heurico 1.16 in 0.000703 seconds.