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

generates a code of length 78 over Z3[X]/(X^3) who´s minimum homogenous weight is 155.

Homogenous weight enumerator: w(x)=1x^0+48x^155+172x^156+12x^159+2x^162+6x^173+2x^183

The gray image is a linear code over GF(3) with n=702, k=5 and d=465.
This code was found by Heurico 1.16 in 0.176 seconds.