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

generates a code of length 46 over Z3[X]/(X^2) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+108x^87+222x^90+324x^93+18x^96+18x^99+36x^105+2x^135

The gray image is a linear code over GF(3) with n=138, k=6 and d=87.
This code was found by Heurico 1.16 in 99.3 seconds.