The generator matrix

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

generates a code of length 57 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 109.

Homogenous weight enumerator: w(x)=1x^0+318x^109+534x^110+754x^111+1008x^112+630x^113+618x^114+648x^115+390x^116+580x^117+510x^118+378x^119+54x^120+84x^121+12x^122+6x^124+12x^127+8x^129+6x^132+6x^133+4x^135

The gray image is a code over GF(3) with n=513, k=8 and d=327.
This code was found by Heurico 1.16 in 0.155 seconds.