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

generates a code of length 78 over Z3[X]/(X^3) who´s minimum homogenous weight is 157.

Homogenous weight enumerator: w(x)=1x^0+66x^157+2x^159+6x^160+4x^165+2x^168

The gray image is a linear code over GF(3) with n=702, k=4 and d=471.
This code was found by Heurico 1.16 in 0.176 seconds.