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

generates a code of length 83 over Z3[X]/(X^3) who´s minimum homogenous weight is 159.

Homogenous weight enumerator: w(x)=1x^0+336x^159+660x^162+1458x^164+456x^165+2916x^167+210x^168+222x^171+24x^174+84x^177+168x^180+6x^183+18x^186+2x^243

The gray image is a linear code over GF(3) with n=747, k=8 and d=477.
This code was found by Heurico 1.16 in 33 seconds.