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  X  1  X  1  1  1  1  1  X  X  1  1  1  X  X  X  1  X  1  X  X  3  3  0  X  X  X  X  3  X  1
 0  3  6  0  3  6  0  3  6  0  3  6  0  3  6  0  3  6  0  3  6  0  3  6  0  3  6  0  3  6  3  0  6  3  6  0  3  6  3  6  0  3  6  3  6  0  0  0  3  3  6  3  6  3  0  0  3  6  0  0  6

generates a code of length 61 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 123.

Homogenous weight enumerator: w(x)=1x^0+72x^123+2x^126+6x^129

The gray image is a code over GF(3) with n=549, k=4 and d=369.
This code was found by Heurico 1.16 in 0.0686 seconds.