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  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  X
 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  X 2X
 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  X 2X 2X
 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  X 2X 2X 2X

generates a code of length 86 over Z3[X]/(X^2) who´s minimum homogenous weight is 165.

Homogenous weight enumerator: w(x)=1x^0+10x^165+40x^168+80x^171+486x^172+80x^174+30x^177+2x^258

The gray image is a linear code over GF(3) with n=258, k=6 and d=165.
This code was found by Heurico 1.16 in 0.102 seconds.