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

generates a code of length 40 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+348x^78+272x^81+90x^84+12x^87+6x^90

The gray image is a code over GF(3) with n=360, k=6 and d=234.
This code was found by Heurico 1.16 in 0.0224 seconds.