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

generates a code of length 83 over Z3[X]/(X^3) who´s minimum homogenous weight is 165.

Homogenous weight enumerator: w(x)=1x^0+148x^165+54x^167+6x^168+8x^171+26x^174

The gray image is a linear code over GF(3) with n=747, k=5 and d=495.
This code was found by Heurico 1.16 in 0.226 seconds.