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

generates a code of length 84 over Z3[X]/(X^2) who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+80x^162+486x^168+160x^171+2x^252

The gray image is a linear code over GF(3) with n=252, k=6 and d=162.
This code was found by Heurico 1.16 in 0.0948 seconds.