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

generates a code of length 77 over Z3[X]/(X^3) who´s minimum homogenous weight is 155.

Homogenous weight enumerator: w(x)=1x^0+54x^155+2x^156+18x^157+2x^159+4x^162

The gray image is a linear code over GF(3) with n=693, k=4 and d=465.
This code was found by Heurico 1.16 in 0.167 seconds.