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

generates a code of length 86 over Z3[X]/(X^2) who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+344x^162+120x^165+282x^168+568x^171+294x^174+258x^177+186x^180+18x^183+66x^189+36x^198+12x^207+2x^225

The gray image is a linear code over GF(3) with n=258, k=7 and d=162.
This code was found by Heurico 1.16 in 80.4 seconds.