The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1
 0  X  0  0  0  0  X 2X 2X  0  X  0  X  X  X  0  X
 0  0  X  0  0  X 2X  0 2X  0  X  X 2X  0 2X 2X  0
 0  0  0  X  0 2X 2X  X  0  X  X 2X 2X  0  0 2X 2X
 0  0  0  0  X 2X 2X 2X 2X 2X 2X  0  0 2X  0 2X 2X

generates a code of length 17 over Z3[X]/(X^2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+34x^27+58x^30+162x^32+52x^33+324x^35+36x^36+26x^39+20x^42+10x^45+6x^48

The gray image is a linear code over GF(3) with n=51, k=6 and d=27.
This code was found by Heurico 1.16 in 0.00315 seconds.