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

generates a code of length 76 over Z3[X]/(X^3) who´s minimum homogenous weight is 151.

Homogenous weight enumerator: w(x)=1x^0+180x^151+18x^154+12x^156+12x^159+18x^160+2x^162

The gray image is a linear code over GF(3) with n=684, k=5 and d=453.
This code was found by Heurico 1.16 in 0.405 seconds.