The generator matrix

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

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+32x^27+270x^28+498x^29+614x^30+1008x^31+1458x^32+1164x^33+954x^34+450x^35+36x^36+36x^37+24x^38+16x^39

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 0.0234 seconds.