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

generates a code of length 91 over Z3[X]/(X^3) who´s minimum homogenous weight is 183.

Homogenous weight enumerator: w(x)=1x^0+72x^183+6x^192+2x^207

The gray image is a linear code over GF(3) with n=819, k=4 and d=549.
This code was found by Heurico 1.16 in 0.32 seconds.