The generator matrix

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

generates a code of length 61 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 121.

Homogenous weight enumerator: w(x)=1x^0+96x^121+576x^122+48x^124+2x^129+4x^132+2x^156

The gray image is a code over GF(3) with n=549, k=6 and d=363.
This code was found by Heurico 1.16 in 0.0466 seconds.