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

generates a code of length 44 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+222x^79+330x^80+80x^81+576x^82+684x^83+636x^84+684x^85+2502x^86+2130x^87+2814x^88+4092x^89+2092x^90+864x^91+594x^92+84x^93+444x^94+354x^95+66x^96+168x^97+132x^98+12x^99+54x^100+54x^101+6x^103+6x^104+2x^117

The gray image is a code over GF(3) with n=396, k=9 and d=237.
This code was found by Heurico 1.16 in 2.5 seconds.