The generator matrix

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

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+698x^78+1566x^79+5244x^80+7550x^81+12000x^82+18834x^83+26508x^84+35784x^85+51060x^86+60808x^87+63132x^88+72222x^89+62754x^90+47142x^91+34170x^92+17908x^93+8280x^94+4008x^95+1266x^96+228x^97+78x^98+126x^99+24x^100+24x^101+14x^102+12x^104

The gray image is a code over GF(3) with n=396, k=12 and d=234.
This code was found by Heurico 1.16 in 292 seconds.