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

generates a code of length 44 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+340x^81+546x^84+972x^86+1158x^87+1944x^89+1170x^90+162x^93+156x^96+88x^99+12x^102+10x^108+2x^126

The gray image is a code over GF(3) with n=396, k=8 and d=243.
This code was found by Heurico 1.16 in 27.8 seconds.