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

generates a code of length 44 over Z9[X]/(X^2+6,3X) 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 0.521 seconds.