The generator matrix

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

generates a code of length 16 over Z3[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+108x^28+364x^30+444x^31+162x^32+670x^33+408x^34+14x^36+12x^37+2x^39+2x^42

The gray image is a linear code over GF(3) with n=144, k=7 and d=84.
This code was found by Heurico 1.16 in 0.00361 seconds.