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

generates a code of length 82 over Z3[X]/(X^2) who´s minimum homogenous weight is 165.

Homogenous weight enumerator: w(x)=1x^0+72x^165+4x^171+4x^180

The gray image is a linear code over GF(3) with n=246, k=4 and d=165.
This code was found by Heurico 1.16 in 0.065 seconds.