The generator matrix
1 0 1 1 1 1 1 0 1 1 1 X 1 1 1 X 1
0 1 1 2 2X+1 0 2 1 X 2X+1 X+2 1 X X+1 X+2 1 0
0 0 2X 0 X X 2X 2X 2X 0 X X X 2X 2X 2X 0
generates a code of length 17 over Z3[X]/(X^2) who´s minimum homogenous weight is 30.
Homogenous weight enumerator: w(x)=1x^0+22x^30+90x^32+18x^33+36x^35+20x^36+36x^38+20x^39
The gray image is a linear code over GF(3) with n=51, k=5 and d=30.
This code was found by Heurico 1.16 in 0.000755 seconds.