The generator matrix

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

generates a code of length 17 over Z3[X]/(X^2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+70x^27+102x^28+110x^30+294x^31+232x^33+612x^34+180x^36+402x^37+102x^39+48x^40+20x^42+10x^45+4x^48

The gray image is a linear code over GF(3) with n=51, k=7 and d=27.
This code was found by Heurico 1.16 in 0.168 seconds.