The generator matrix

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

generates a code of length 17 over Z3[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+44x^21+148x^24+224x^27+282x^30+390x^33+4374x^34+492x^36+348x^39+162x^42+66x^45+28x^48+2x^51

The gray image is a linear code over GF(3) with n=51, k=8 and d=21.
This code was found by Heurico 1.16 in 0.115 seconds.