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

generates a code of length 83 over Z3[X]/(X^3) who´s minimum homogenous weight is 162.

Homogenous weight enumerator: w(x)=1x^0+80x^162+1944x^166+160x^168+2x^249

The gray image is a linear code over GF(3) with n=747, k=7 and d=486.
This code was found by Heurico 1.16 in 0.339 seconds.