The generator matrix

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

generates a code of length 83 over Z3[X]/(X^2) who´s minimum homogenous weight is 164.

Homogenous weight enumerator: w(x)=1x^0+102x^164+22x^165+30x^167+42x^168+12x^170+8x^171+18x^173+8x^174

The gray image is a linear code over GF(3) with n=249, k=5 and d=164.
This code was found by Heurico 1.16 in 0.0843 seconds.