The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 2X^2 1 X 1 X
0 X 0 X^2 2X 2X^2+X X 2X^2+2X 2X X^2 2X^2 2X^2+X X 2X^2 2X^2+2X 2X X^2
0 0 X 2X^2+2X X^2 2X^2+2X X 2X^2+X X^2+2X X^2 2X^2+X 0 X^2+X X^2+2X 2X^2+X 2X^2+X X
generates a code of length 17 over Z3[X]/(X^3) who´s minimum homogenous weight is 30.
Homogenous weight enumerator: w(x)=1x^0+190x^30+54x^31+252x^32+280x^33+552x^34+372x^35+344x^36+30x^37+12x^38+74x^39+12x^40+12x^41+2x^42
The gray image is a linear code over GF(3) with n=153, k=7 and d=90.
This code was found by Heurico 1.16 in 0.114 seconds.