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

generates a code of length 83 over Z3[X]/(X^2) who´s minimum homogenous weight is 167.

Homogenous weight enumerator: w(x)=1x^0+54x^167+12x^168+8x^171+6x^174

The gray image is a linear code over GF(3) with n=249, k=4 and d=167.
This code was found by Heurico 1.16 in 0.105 seconds.