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

generates a code of length 89 over Z3[X]/(X^3) who´s minimum homogenous weight is 180.

Homogenous weight enumerator: w(x)=1x^0+74x^180+6x^183

The gray image is a linear code over GF(3) with n=801, k=4 and d=540.
This code was found by Heurico 1.16 in 0.293 seconds.