The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  X  0  X  X 2X  0  0  X  X 2X 2X 2X  0
 0  0  X  0 2X  X 2X  X 2X  0  X  X  0  0  0  X 2X
 0  0  0  X 2X 2X  0 2X 2X 2X  X  0 2X  0  X 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+30x^33+162x^34+8x^36+14x^39+4x^42+2x^51

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 0.00119 seconds.