The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  X  X  X  0  X 2X  0  0
 0  0  X  0  0  0  0  0  0 2X  X 2X 2X  0 2X  0  0
 0  0  0  X  0  0  0  0  X 2X  0 2X  X 2X  0  X  0
 0  0  0  0  X  0  0  0 2X 2X  0  X  0 2X  X  X  0
 0  0  0  0  0  X  0  0 2X 2X  X  0 2X  X  X  X  0
 0  0  0  0  0  0  X  0 2X 2X 2X  X  X  X 2X  X  0
 0  0  0  0  0  0  0  X 2X  0  X 2X  X  0  X  0  0

generates a code of length 17 over Z3[X]/(X^2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+70x^18+196x^21+338x^24+574x^27+980x^30+1274x^33+13122x^34+1202x^36+962x^39+596x^42+286x^45+76x^48+6x^51

The gray image is a linear code over GF(3) with n=51, k=9 and d=18.
This code was found by Heurico 1.16 in 0.579 seconds.