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

generates a code of length 40 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+12x^78+210x^80+8x^81+4x^84+6x^89+2x^93

The gray image is a code over GF(3) with n=360, k=5 and d=234.
This code was found by Heurico 1.16 in 0.014 seconds.