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  X  X  0  1  1  X  X X^2  1  1  1  1  1  X  X 2X^2  1  1  1  1  1  1  1  1  1  1  1  X  X  0  X  X X^2  X  X 2X^2  X  X  X  X  X  1  1
 0  X 2X X^2 2X^2+X X^2+2X 2X^2 X^2+X 2X^2+2X  0 2X^2+X 2X X^2 X^2+X X^2+2X 2X^2  X 2X^2+2X  0 2X^2+X 2X X^2 X^2+X X^2+2X 2X^2  X 2X^2+2X  0 2X^2+X 2X X^2 X^2+X X^2+2X 2X^2  X 2X^2+2X 2X^2+X 2X  X  0 2X^2+X X^2+X X^2+2X  X 2X X^2 X^2+X X^2+2X 2X^2  X 2X^2+2X  X  X 2X^2+2X  0 X^2 2X^2 2X^2+X X^2+X  X 2X X^2+2X 2X^2+2X 2X^2+X 2X  X X^2+X X^2+2X  X  X 2X^2+2X  X  0 X^2 2X^2 2X^2+X X^2+X  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+54x^157+144x^158+24x^160+12x^163+4x^168+4x^174

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 0.184 seconds.