The generator matrix

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

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+176x^18+426x^21+910x^24+1760x^27+3144x^30+13122x^32+3870x^33+26244x^35+3912x^36+2910x^39+1680x^42+712x^45+162x^48+20x^51

The gray image is a linear code over GF(3) with n=51, k=10 and d=18.
This code was found by Heurico 1.16 in 3.77 seconds.