The generator matrix

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

generates a code of length 83 over Z3[X]/(X^3) who´s minimum homogenous weight is 155.

Homogenous weight enumerator: w(x)=1x^0+534x^155+1108x^156+1998x^157+4320x^158+5076x^159+5760x^160+9354x^161+9826x^162+11682x^163+14538x^164+14540x^165+15678x^166+16638x^167+15024x^168+12798x^169+12402x^170+9164x^171+6138x^172+5064x^173+2474x^174+1278x^175+996x^176+216x^177+72x^178+174x^179+80x^180+72x^182+58x^183+42x^185+24x^186+12x^188+6x^191

The gray image is a linear code over GF(3) with n=747, k=11 and d=465.
This code was found by Heurico 1.16 in 89.1 seconds.