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

generates a code of length 89 over Z3[X]/(X^3) who´s minimum homogenous weight is 177.

Homogenous weight enumerator: w(x)=1x^0+192x^177+486x^178+24x^180+18x^186+2x^189+6x^204

The gray image is a linear code over GF(3) with n=801, k=6 and d=531.
This code was found by Heurico 1.16 in 0.302 seconds.