The generator matrix

 1  0  0  1  1  1  1  1  1  3  1  1 X+3  1  X 2X+3  1  1  1  1  6  1  1  1  6  1  1  1  1  1  1 2X+6 2X+3  1  1 2X  6 X+6  1  1  1 2X  1  X  1  1  1  1  1  1  1  1 2X+6  6  1  1
 0  1  0  3  1  4  2  X  8  1 2X+4 2X+2  1 X+3  1 2X+6  6 X+6  2 2X+7 2X+6 2X X+2 X+8  1 X+1  0 X+7 X+5 2X+1 2X+5  1  1 X+4 2X+4  1  1  1  5 2X+3 2X+3  3  1  1  2  3 2X+6  7 2X+2  8 X+8 X+6  1 X+6 2X+1 2X
 0  0  1 2X+4 2X+1  3 X+8 X+5 2X+6  4 2X+2  4  2 2X X+6  1  7 2X+8  5  2  1 X+3  4 2X+6 2X+7 X+7 2X+5 2X+2 X+4 2X  5  8 X+3 2X+7  X  6 2X+5 X+4  3 X+5 X+1  1  4 2X+1 X+7 X+6  0  2 X+6 X+6  X  6  4  1 X+4 2X+7

generates a code of length 56 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 106.

Homogenous weight enumerator: w(x)=1x^0+552x^106+1284x^107+1392x^108+1980x^109+2286x^110+1760x^111+2418x^112+1860x^113+1168x^114+1308x^115+1314x^116+824x^117+858x^118+528x^119+116x^120+18x^122+2x^123+12x^127+2x^129

The gray image is a code over GF(3) with n=504, k=9 and d=318.
This code was found by Heurico 1.16 in 0.587 seconds.