The generator matrix
1 1 1 1 1 1 1 1 1 1 1 X X X 1 X X
0 X^2 2X^2 0 X^2 2X^2 0 X^2 2X^2 0 X^2 X^2 2X^2 0 2X^2 X^2 0
generates a code of length 17 over Z3[X]/(X^3) who´s minimum homogenous weight is 33.
Homogenous weight enumerator: w(x)=1x^0+12x^33+54x^34+8x^36+6x^39
The gray image is a linear code over GF(3) with n=153, k=4 and d=99.
This code was found by Heurico 1.16 in 0.00074 seconds.