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

generates a code of length 44 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+200x^84+174x^85+282x^86+324x^87+330x^88+336x^89+294x^90+126x^91+22x^93+6x^94+24x^95+24x^96+12x^97+6x^98+24x^99+2x^117

The gray image is a code over GF(3) with n=396, k=7 and d=252.
This code was found by Heurico 1.16 in 0.524 seconds.