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

generates a code of length 84 over Z3[X]/(X^2) who´s minimum homogenous weight is 165.

Homogenous weight enumerator: w(x)=1x^0+132x^165+28x^168+18x^171+60x^174+2x^186+2x^225

The gray image is a linear code over GF(3) with n=252, k=5 and d=165.
This code was found by Heurico 1.16 in 2.24 seconds.