The generator matrix

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

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+134x^27+54x^28+1194x^30+324x^31+2916x^32+3888x^33+648x^34+5832x^35+3930x^36+432x^37+312x^39+12x^45+6x^48

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 3.33 seconds.