The generator matrix

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

generates a code of length 17 over Z3[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+126x^26+66x^27+318x^28+726x^29+2220x^30+870x^31+8328x^32+8656x^33+10548x^34+15732x^35+8612x^36+1266x^37+1254x^38+94x^39+120x^40+78x^41+20x^42+6x^45+8x^48

The gray image is a linear code over GF(3) with n=153, k=10 and d=78.
This code was found by Heurico 1.16 in 1.6 seconds.