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

generates a code of length 35 over Z3[X]/(X^2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+66x^51+224x^54+346x^57+490x^60+162x^62+604x^63+1296x^65+752x^66+3888x^68+842x^69+5184x^71+946x^72+2592x^74+784x^75+652x^78+430x^81+264x^84+108x^87+36x^90+14x^93+2x^96

The gray image is a linear code over GF(3) with n=105, k=9 and d=51.
This code was found by Heurico 1.16 in 4.52 seconds.