The generator matrix

 1  0  1  1  1  1  1 X+3  1  1  1 2X  1  1  1  6  1  1  1 X+6  1  1  1 2X+6  1  1  1  1  1  1  1  1  1  3  X 2X+3  1  1  1  1
 0  1 2X+4  8 X+3 X+1 X+2  1 2X  4 2X+8  1  6 2X+7  5  1 X+6 X+7 X+5  1 2X+6  7 2X+5  1  3 2X+1  X X+4 2X+3  1  2 X+8 2X+2  1  1  1  0 X+3 2X  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+42x^78+36x^79+540x^80+86x^81+18x^82+6x^93

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 0.0103 seconds.