The generator matrix

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

generates a code of length 17 over Z3[X]/(X^3) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+152x^27+246x^28+354x^29+630x^30+366x^31+2442x^32+1408x^33+6444x^34+4482x^35+1586x^36+582x^37+438x^38+330x^39+138x^40+60x^41+20x^42+4x^45

The gray image is a linear code over GF(3) with n=153, k=9 and d=81.
This code was found by Heurico 1.16 in 0.361 seconds.