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

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+276x^78+54x^79+108x^80+702x^81+216x^82+216x^83+432x^84+54x^85+42x^87+60x^90+18x^93+6x^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 0.0327 seconds.