The generator matrix

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

generates a code of length 57 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 113.

Homogenous weight enumerator: w(x)=1x^0+216x^113+396x^114+108x^116+2x^117+4x^126+2x^144

The gray image is a code over GF(3) with n=513, k=6 and d=339.
This code was found by Heurico 1.16 in 0.0364 seconds.