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

generates a code of length 57 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+56x^114+6x^116+4x^117+6x^119+2x^120+6x^122

The gray image is a code over GF(3) with n=513, k=4 and d=342.
This code was found by Heurico 1.16 in 0.0527 seconds.