The generator matrix

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

generates a code of length 34 over Z3[X]/(X^2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+186x^51+312x^54+454x^57+722x^60+2002x^63+4684x^66+6046x^69+3518x^72+778x^75+496x^78+282x^81+126x^84+56x^87+12x^90+6x^93+2x^99

The gray image is a linear code over GF(3) with n=102, k=9 and d=51.
This code was found by Heurico 1.16 in 16.8 seconds.