The generator matrix

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

generates a code of length 86 over Z3[X]/(X^3) who´s minimum homogenous weight is 161.

Homogenous weight enumerator: w(x)=1x^0+300x^161+394x^162+792x^163+1590x^164+1352x^165+2538x^166+2772x^167+3000x^168+4680x^169+3876x^170+4196x^171+6606x^172+4740x^173+4584x^174+5706x^175+3504x^176+2328x^177+2610x^178+1458x^179+652x^180+378x^181+402x^182+106x^183+18x^184+180x^185+70x^186+72x^188+56x^189+54x^191+20x^192+6x^194+2x^195+2x^201+2x^207+2x^210

The gray image is a linear code over GF(3) with n=774, k=10 and d=483.
This code was found by Heurico 1.16 in 13.6 seconds.