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

generates a code of length 85 over Z3[X]/(X^3) who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+296x^162+108x^164+528x^165+648x^167+828x^168+1296x^170+1292x^171+864x^173+318x^174+84x^177+126x^180+144x^183+24x^186+2x^189+2x^234

The gray image is a linear code over GF(3) with n=765, k=8 and d=486.
This code was found by Heurico 1.16 in 0.831 seconds.