The generator matrix

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

generates a code of length 81 over Z3[X]/(X^2) who´s minimum homogenous weight is 146.

Homogenous weight enumerator: w(x)=1x^0+678x^146+524x^147+1758x^149+1044x^150+2988x^152+1818x^153+4182x^155+2388x^156+5154x^158+2616x^159+5622x^161+2770x^162+5604x^164+2874x^165+5478x^167+2448x^168+4032x^170+1632x^171+2454x^173+1000x^174+996x^176+420x^177+372x^179+120x^180+42x^182+18x^183+6x^185+6x^186+4x^189

The gray image is a linear code over GF(3) with n=243, k=10 and d=146.
This code was found by Heurico 1.16 in 124 seconds.