The generator matrix

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

generates a code of length 17 over Z3[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+94x^24+36x^26+174x^27+288x^29+346x^30+2808x^32+568x^33+8748x^34+5040x^35+442x^36+576x^38+454x^39+88x^42+4x^45+10x^48+6x^51

The gray image is a linear code over GF(3) with n=153, k=9 and d=72.
This code was found by Heurico 1.16 in 0.322 seconds.