The generator matrix

 1  0  0  0  1  1  1 2X  1  1  1  1  1  1  0 2X  1
 0  1  0  0 2X  1 2X+1  1  0 2X  1 X+1 2X+2 2X+1  1  1 X+1
 0  0  1  0 2X+1  1 2X+2 X+1  X  2 X+2  X  2 X+2 2X+2  1 2X+1
 0  0  0  1 2X+2  X X+2 X+2  1  2 2X+1 2X 2X+2  X 2X  1  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+248x^27+168x^28+276x^29+574x^30+222x^31+366x^32+1138x^33+540x^34+432x^35+1126x^36+498x^37+336x^38+506x^39+30x^40+48x^41+50x^42+2x^45

The gray image is a linear code over GF(3) with n=51, k=8 and d=27.
This code was found by Heurico 1.16 in 0.11 seconds.