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  X  1  1  1  1 2X^2  1  1  X  1  1  1  X  1  1  1  1  1  X  1  X  0  X
 0  X  0  0 2X 2X^2+X  X 2X^2+2X 2X X^2 2X^2 2X^2+X 2X^2+X 2X^2+2X 2X 2X^2 X^2+X 2X^2+2X  X 2X^2+X  X 2X X^2 X^2+2X  0 2X^2+X 2X^2+2X  X  X 2X^2 2X^2 X^2 X^2+X X^2+X X^2+2X X^2+2X  0 X^2 2X^2+X X^2+2X X^2+2X  X X^2 X^2+2X 2X^2+2X X^2+2X X^2  0  0 X^2+X 2X^2+2X 2X^2+X 2X^2  0 2X^2+X 2X X^2+2X 2X^2  X  0 2X^2+2X X^2 2X X^2 X^2+X  X 2X X^2 2X  0 2X 2X^2+X  X 2X^2+X 2X^2 X^2 2X^2 2X^2+2X 2X^2+X 2X^2 2X^2+X  X X^2+X
 0  0  X 2X X^2 2X^2+2X  X 2X^2+X X^2+2X 2X^2+2X  0 2X^2+2X X^2 2X X^2  X  X X^2+X 2X  0 X^2+X 2X 2X^2+2X X^2+X X^2+X  0 2X^2 2X^2+2X  X  0 2X^2+2X X^2 2X^2+X 2X^2 X^2+2X  X X^2+2X 2X^2+X X^2+2X 2X^2 X^2+X X^2+X 2X^2 2X^2 2X^2+2X X^2 X^2 X^2+2X X^2+X 2X^2+X  X 2X^2 X^2+X  0 X^2+2X X^2+2X X^2+2X X^2 2X^2  X 2X^2+X  X 2X^2 2X^2 2X^2+2X 2X^2+X 2X^2+X X^2+2X  0 2X^2+2X  0 X^2 X^2+X 2X^2+X X^2+2X X^2+2X 2X^2+2X 2X^2+X 2X X^2+X X^2  0 X^2
 0  0  0 X^2  0  0  0  0  0  0 2X^2 X^2 2X^2 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 2X^2 2X^2 X^2 X^2  0 X^2 2X^2 2X^2 2X^2 2X^2 X^2  0 2X^2  0  0 X^2 X^2  0  0 2X^2  0 2X^2  0  0  0  0 2X^2 X^2 X^2  0 X^2  0 X^2  0 2X^2 2X^2  0 2X^2  0 X^2 2X^2  0 2X^2  0 X^2 2X^2  0 X^2 X^2  0 X^2 X^2 X^2 2X^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+400x^159+36x^160+144x^161+820x^162+216x^163+216x^164+1490x^165+432x^166+432x^167+1410x^168+288x^169+180x^170+164x^171+106x^174+74x^177+102x^180+24x^183+24x^186+2x^225

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 3 seconds.