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

generates a code of length 53 over Z9[X]/(X^2+6,3X) who´s minimum homogenous weight is 106.

Homogenous weight enumerator: w(x)=1x^0+54x^106+14x^108+8x^111+2x^114+2x^117

The gray image is a code over GF(3) with n=477, k=4 and d=318.
This code was found by Heurico 1.16 in 0.04 seconds.