The generator matrix

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

generates a code of length 83 over Z3[X]/(X^3) who´s minimum homogenous weight is 161.

Homogenous weight enumerator: w(x)=1x^0+600x^161+858x^162+378x^163+918x^164+712x^165+324x^166+636x^167+558x^168+180x^169+474x^170+438x^171+72x^172+252x^173+92x^174+18x^175+18x^176+6x^180+2x^183+12x^185+6x^188+2x^189+4x^192

The gray image is a linear code over GF(3) with n=747, k=8 and d=483.
This code was found by Heurico 1.16 in 0.394 seconds.