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

generates a code of length 51 over Z9[X]/(X^2+3,3X) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+100x^96+164x^99+1674x^102+202x^105+16x^108+16x^114+6x^117+6x^123+2x^144

The gray image is a code over GF(3) with n=459, k=7 and d=288.
This code was found by Heurico 1.16 in 0.183 seconds.