The generator matrix

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

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+630x^28+468x^29+1782x^30+3396x^31+6372x^32+6436x^33+15732x^34+12420x^35+6488x^36+4428x^37+666x^38+106x^39+114x^40+8x^42+2x^48

The gray image is a linear code over GF(3) with n=153, k=10 and d=84.
This code was found by Heurico 1.16 in 1.44 seconds.