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  X  1  1  X  X  0  X  1
 0  X 2X  0 X+3 2X X+3 2X+6  0  6  0  6 X+3 X+6  6 2X  3 2X+6 X+3 2X+6 X+6 2X+6 X+6 2X+3 X+6 2X  6 X+3 X+3  X  3 X+6  0  0  3  6 X+3 2X  X 2X 2X
 0  0  6  0  6  0  3  3  6  3  6  3  3  0  6  0  3  6  6  3  0  0  6  3  3  6  0  3  6  0  0  0  3  0  6  6  6  0  6  0  3
 0  0  0  6  3  6  6  3  3  6  0  3  3  3  6  3  0  3  0  6  0  6  0  6  3  3  3  0  6  6  0  6  6  6  3  0  0  6  6  0  0

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

Homogenous weight enumerator: w(x)=1x^0+310x^78+324x^80+414x^81+648x^83+354x^84+64x^87+42x^90+24x^93+4x^96+2x^108

The gray image is a code over GF(3) with n=369, k=7 and d=234.
This code was found by Heurico 1.16 in 21.5 seconds.