The generator matrix

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

generates a code of length 17 over Z3[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+132x^28+180x^29+204x^30+180x^31+1278x^32+746x^33+288x^34+2160x^35+734x^36+300x^37+198x^38+6x^39+72x^40+72x^41+4x^42+6x^45

The gray image is a linear code over GF(3) with n=153, k=8 and d=84.
This code was found by Heurico 1.16 in 4.21 seconds.