The generator matrix

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

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+136x^27+792x^28+1260x^29+1954x^30+2544x^31+5100x^32+3564x^33+2796x^34+1248x^35+250x^36+24x^37+6x^38+8x^39

The gray image is a linear code over GF(3) with n=144, k=9 and d=81.
This code was found by Heurico 1.16 in 0.157 seconds.