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

generates a code of length 53 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+112x^96+150x^97+258x^98+462x^99+408x^100+534x^101+882x^102+618x^103+2250x^104+2418x^105+2568x^106+3894x^107+2426x^108+678x^109+480x^110+328x^111+204x^112+156x^113+266x^114+144x^115+132x^116+130x^117+84x^118+48x^119+20x^120+6x^121+24x^122+2x^144

The gray image is a code over GF(3) with n=477, k=9 and d=288.
This code was found by Heurico 1.16 in 1.52 seconds.