The generator matrix

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

generates a code of length 16 over Z3[X]/(X^3) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+110x^27+324x^28+1184x^30+1296x^31+2178x^33+1296x^34+150x^36+20x^39+2x^48

The gray image is a linear code over GF(3) with n=144, k=8 and d=81.
This code was found by Heurico 1.16 in 0.0241 seconds.