The generator matrix

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

generates a code of length 83 over Z3[X]/(X^3) who´s minimum homogenous weight is 160.

Homogenous weight enumerator: w(x)=1x^0+108x^160+240x^161+1314x^162+612x^163+216x^164+1038x^165+522x^166+120x^167+664x^168+252x^169+66x^170+872x^171+288x^172+144x^173+72x^174+24x^176+2x^177+2x^183+4x^201

The gray image is a linear code over GF(3) with n=747, k=8 and d=480.
This code was found by Heurico 1.16 in 0.387 seconds.