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  X  X  0  1  1  X  X  6  1  1  X  X  3  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X 2X  6 X+3 2X+6  3 X+6 2X+3  0 X+3 2X  6 X+6 2X+6  3  X 2X+3  0 X+3 2X  6 X+6 2X+6  3  X 2X+3  0 X+3 X+3 2X  X  6 X+6 X+6 2X+6  X  3  X  X 2X+3  X 2X 2X+6 2X+3  0  6  3 X+3 X+6  X 2X 2X+6 2X+3  0  6  3 X+3 X+6  X

generates a code of length 60 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 120.

Homogenous weight enumerator: w(x)=1x^0+234x^120+4x^126+2x^135+2x^153

The gray image is a code over GF(3) with n=540, k=5 and d=360.
This code was found by Heurico 1.16 in 0.0639 seconds.