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

generates a code of length 78 over Z3[X]/(X^3) who´s minimum homogenous weight is 154.

Homogenous weight enumerator: w(x)=1x^0+102x^154+522x^156+54x^157+36x^159+8x^162+6x^181

The gray image is a linear code over GF(3) with n=702, k=6 and d=462.
This code was found by Heurico 1.16 in 0.282 seconds.