The generator matrix

 1  0  1  1  1  1  1 2X^2  1  1  1 2X  1  1  0 X^2  1
 0  1  1  2  0 2X+1 2X^2+2  1 2X^2+2X 2X^2+2X+2 X+1  1 2X^2+X+2 X^2+2X+1  1  X 2X^2
 0  0 2X  0 X^2  X 2X^2+X X^2+X X^2+X 2X^2+2X 2X^2  0 X^2 2X^2+X  X  0 2X^2+X
 0  0  0  X 2X^2+2X 2X^2 X^2+2X 2X 2X^2+2X  X X^2+2X X^2+2X 2X 2X 2X^2+X 2X^2+X 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+246x^27+528x^28+528x^29+2458x^30+2016x^31+7596x^32+8158x^33+10494x^34+14328x^35+8150x^36+2928x^37+876x^38+638x^39+72x^40+32x^42

The gray image is a linear code over GF(3) with n=153, k=10 and d=81.
This code was found by Heurico 1.16 in 1.75 seconds.