The generator matrix

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

generates a code of length 16 over Z3[X]/(X^3) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+12x^31+54x^32+4x^33+6x^34+2x^36+2x^42

The gray image is a linear code over GF(3) with n=144, k=4 and d=93.
This code was found by Heurico 1.16 in 0.000601 seconds.