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  1  1  1  1  1  1  X  1  X  1  1  1  1  X  X  X  X  X  3  1
 0  3  0  0  3  0  3  3  6  0  0  3  3  0  6  3  6  6  0  3  6  0  3  6  6  6  6  0  0  0  3  3  0  3  3  6  3  0  0  3  3  0  6  3  0  6  0  3  3  3  3  6  3  6  6  3  6
 0  0  3  0  6  3  6  3  6  0  3  3  0  6  0  0  3  3  6  6  6  6  3  0  0  3  6  0  0  3  6  3  3  6  0  6  0  0  3  3  0  6  0  3  6  3  6  6  3  0  6  3  3  0  0  3  0
 0  0  0  3  6  6  0  6  6  6  3  0  6  0  6  3  3  0  3  3  3  6  3  0  3  6  0  0  3  6  6  6  3  3  3  6  6  6  0  0  0  3  3  3  0  0  6  0  3  6  6  6  0  0  6  6  0

generates a code of length 57 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+126x^111+162x^112+36x^114+324x^115+22x^117+54x^120+2x^135+2x^144

The gray image is a code over GF(3) with n=513, k=6 and d=333.
This code was found by Heurico 1.16 in 0.173 seconds.