The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1  X
 0  X 2X  0 2X^2+X 2X  0 2X^2+X 2X X^2  0 2X^2 2X^2+X 2X  0 X^2 2X^2+X
 0  0 X^2  0  0  0 X^2 2X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2
 0  0  0 X^2  0 X^2 X^2 2X^2 X^2  0 2X^2 X^2 2X^2 2X^2 X^2  0  0
 0  0  0  0 2X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2  0 2X^2 2X^2 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+84x^27+54x^28+342x^30+324x^31+486x^32+742x^33+2106x^34+972x^35+848x^36+432x^37+124x^39+32x^42+12x^45+2x^48

The gray image is a linear code over GF(3) with n=153, k=8 and d=81.
This code was found by Heurico 1.16 in 0.0564 seconds.