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  X  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1 2X^2  X  1  X
 0  X  0  0 2X 2X^2+X  X 2X^2+2X 2X X^2 2X^2 2X^2+X 2X^2+X 2X^2+2X 2X 2X^2 X^2+X 2X^2+2X  X 2X^2+X  X 2X X^2 X^2+2X  0 2X^2+X 2X^2+2X  X  X 2X^2 2X^2 X^2 X^2+X X^2+X X^2+2X X^2+2X  0 X^2 2X^2+X X^2+2X X^2+2X  X X^2 X^2+2X 2X^2+2X  0 2X^2+2X X^2 X^2+2X X^2+X  0 2X^2+X 2X^2  0 2X^2+X 2X X^2+2X 2X^2  X  0 2X^2+2X X^2 2X^2+2X 2X^2 2X 2X^2+2X X^2+X 2X^2 2X^2+2X 2X^2+2X X^2 2X X^2+2X X^2+2X  0 X^2 X^2+X 2X^2 2X^2+2X X^2+2X X^2+X 2X^2+2X  X 2X 2X^2 2X
 0  0  X 2X X^2 2X^2+2X  X 2X^2+X X^2+2X 2X^2+2X  0 2X^2+2X X^2 2X X^2  X  X X^2+X 2X  0 X^2+X 2X 2X^2+2X X^2+X X^2+X  0 2X^2 2X^2+2X  X  0 2X^2+2X X^2 2X^2+X 2X^2 X^2+2X  X X^2+2X 2X^2+X X^2+2X 2X^2 X^2+X X^2+X 2X^2 2X^2 2X^2+2X X^2+2X  X X^2 X^2 2X^2+X X^2+X 2X^2 X^2+X  0 X^2+2X X^2+2X X^2+2X X^2 2X^2  X 2X^2+X  X X^2 2X^2+2X  0 2X 2X^2+2X X^2  0  X X^2 2X^2+2X X^2+2X X^2+X 2X^2+2X 2X^2+X  X X^2+2X 2X^2+X 2X^2+X X^2+2X 2X^2 2X^2+X 2X^2 2X  0
 0  0  0 X^2  0  0  0  0  0  0 2X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 X^2  0 X^2 2X^2 2X^2 2X^2 2X^2 X^2  0 2X^2  0  0 X^2 X^2  0  0  0 2X^2  0  0 2X^2  0  0 2X^2 X^2 X^2  0 X^2  0 X^2  0 2X^2 2X^2  0 X^2  0 2X^2  0 X^2 X^2 X^2 2X^2 X^2 2X^2 X^2  0 2X^2  0 X^2 2X^2 X^2  0  0  0 X^2 X^2

generates a code of length 86 over Z3[X]/(X^3) who´s minimum homogenous weight is 165.

Homogenous weight enumerator: w(x)=1x^0+432x^165+18x^166+54x^167+612x^168+108x^169+810x^170+876x^171+702x^172+1458x^173+706x^174+144x^175+108x^176+166x^177+136x^180+104x^183+68x^186+56x^189+2x^243

The gray image is a linear code over GF(3) with n=774, k=8 and d=495.
This code was found by Heurico 1.16 in 3.57 seconds.