The generator matrix

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

generates a code of length 17 over Z3[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+72x^28+156x^29+72x^30+276x^31+264x^32+64x^33+306x^34+324x^35+62x^36+216x^37+204x^38+34x^39+102x^40+24x^41+8x^42+2x^48

The gray image is a linear code over GF(3) with n=51, k=7 and d=28.
This code was found by Heurico 1.13 in 0.00657 seconds.