The generator matrix

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

generates a code of length 17 over Z3[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+210x^28+84x^29+922x^30+1134x^31+1770x^32+2970x^33+4464x^34+3366x^35+3042x^36+1410x^37+96x^38+98x^39+72x^40+30x^41+12x^42+2x^45

The gray image is a linear code over GF(3) with n=153, k=9 and d=84.
This code was found by Heurico 1.16 in 0.214 seconds.