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

generates a code of length 72 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 144.

Homogenous weight enumerator: w(x)=1x^0+234x^144+6x^153+2x^189

The gray image is a code over GF(3) with n=648, k=5 and d=432.
This code was found by Heurico 1.16 in 0.129 seconds.