The generator matrix

 1  0  0  1  1  1  1  1  1 X+3 2X  1  1  1  0 2X+3  1  1  1  1  6  1  1  1  X  1  1  1  1  1  6  1  1  1  3  1  1  1  1  1 X+3  1  3  1
 0  1  0  1  3  1 X+8  0 2X+4  1  1 2X+2 2X+2  8  1  1 X+4 X+2 2X+6  3  1 2X X+8 2X+1 2X+3  X  2 2X+6  1 2X+5  1  7  7 2X+8  1 2X+5  6 2X+1 2X+4  7  1 X+2  1  0
 0  0  1  8 2X+4  1 X+1  8  3  2 X+1  3 2X+2 2X X+7  6 2X+4 2X+5  8 2X+7  2 2X+6 X+5  X  1  4 2X+1 2X 2X+2  X  5 2X+1 X+6 2X+8 2X+4  3  2  1 2X+7 2X+5  6  6 2X+7  X
 0  0  0 2X  3 2X+3 X+3 2X+6  6  3 2X+3 X+6  X  3  3  X  6  6 X+3 2X+3 2X+3 2X+6 2X+3 2X+6 X+3 X+6 2X X+6 X+3 X+3 X+3  6  X  6  X  3 X+6 X+3 2X X+6 X+6 2X  6  X

generates a code of length 44 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+160x^78+360x^79+1686x^80+2416x^81+4014x^82+6798x^83+9262x^84+10992x^85+17640x^86+19694x^87+21552x^88+24702x^89+21342x^90+14304x^91+11838x^92+5702x^93+2436x^94+1404x^95+360x^96+228x^97+72x^98+100x^99+60x^100+12x^101+12x^102

The gray image is a code over GF(3) with n=396, k=11 and d=234.
This code was found by Heurico 1.16 in 36.9 seconds.