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

generates a code of length 86 over Z3[X]/(X^3) who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+590x^162+36x^164+1200x^165+90x^166+324x^167+1686x^168+486x^169+1836x^170+2794x^171+1674x^172+2988x^173+2538x^174+666x^175+648x^176+900x^177+434x^180+360x^183+234x^186+112x^189+78x^192+6x^195+2x^234

The gray image is a linear code over GF(3) with n=774, k=9 and d=486.
This code was found by Heurico 1.16 in 4.27 seconds.