The generator matrix
1 1 1 1 1 1 1 1 1 1 1 X 1 1 1 1 1
0 X 0 2X^2+X 0 X 2X 2X^2+2X 2X 0 2X^2 X^2 2X X^2+2X 0 2X X^2
0 0 X X^2+2X 2X X 0 2X^2+X 2X 0 2X^2+X X X^2 X^2 X^2+2X X^2 2X^2
0 0 0 X^2 0 2X^2 0 X^2 2X^2 X^2 X^2 X^2 2X^2 X^2 X^2 X^2 X^2
0 0 0 0 X^2 X^2 2X^2 X^2 X^2 X^2 0 X^2 X^2 X^2 2X^2 2X^2 0
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+96x^26+194x^27+456x^29+404x^30+2670x^32+532x^33+8748x^34+4656x^35+652x^36+786x^38+348x^39+84x^41+44x^42+8x^45+4x^48
The gray image is a linear code over GF(3) with n=153, k=9 and d=78.
This code was found by Heurico 1.16 in 0.338 seconds.