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

generates a code of length 86 over Z3[X]/(X^3) who´s minimum homogenous weight is 159.

Homogenous weight enumerator: w(x)=1x^0+144x^159+78x^160+6x^161+446x^162+198x^163+66x^164+436x^165+402x^166+192x^167+1486x^168+1134x^169+342x^170+4316x^171+2154x^172+474x^173+4366x^174+1458x^175+294x^176+446x^177+138x^178+84x^179+322x^180+96x^181+194x^183+84x^184+120x^186+54x^187+60x^189+36x^190+20x^192+14x^195+10x^198+2x^201+4x^204+2x^207+2x^210+2x^237

The gray image is a linear code over GF(3) with n=774, k=9 and d=477.
This code was found by Heurico 1.16 in 10.1 seconds.