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

generates a code of length 79 over Z3[X]/(X^3) who´s minimum homogenous weight is 157.

Homogenous weight enumerator: w(x)=1x^0+48x^157+162x^158+16x^159+8x^162+6x^175+2x^186

The gray image is a linear code over GF(3) with n=711, k=5 and d=471.
This code was found by Heurico 1.16 in 0.185 seconds.