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

generates a code of length 62 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 121.

Homogenous weight enumerator: w(x)=1x^0+96x^121+144x^122+10x^123+78x^124+288x^125+8x^126+96x^127+6x^129+2x^168

The gray image is a code over GF(3) with n=558, k=6 and d=363.
This code was found by Heurico 1.16 in 0.0999 seconds.