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

generates a code of length 41 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+30x^78+54x^80+20x^81+486x^82+108x^83+12x^84+6x^87+6x^90+4x^93+2x^120

The gray image is a code over GF(3) with n=369, k=6 and d=234.
This code was found by Heurico 1.16 in 0.0182 seconds.