The generator matrix

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

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+140x^78+114x^79+402x^80+1104x^81+1170x^82+1770x^83+3396x^84+4158x^85+5454x^86+6786x^87+7506x^88+7830x^89+7068x^90+5352x^91+3162x^92+2138x^93+504x^94+288x^95+320x^96+120x^97+48x^98+152x^99+30x^100+28x^102+8x^105

The gray image is a code over GF(3) with n=396, k=10 and d=234.
This code was found by Heurico 1.16 in 6.28 seconds.