The generator matrix

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

generates a code of length 17 over Z3[X]/(X^3) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+274x^30+324x^32+374x^33+648x^35+456x^36+102x^39+4x^42+2x^45+2x^48

The gray image is a linear code over GF(3) with n=153, k=7 and d=90.
This code was found by Heurico 1.16 in 77 seconds.