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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  X a*X a*X a^2*X a^5*X  0  X a*X 2*X a^2*X 2*X a^2*X a^3*X a^5*X 2*X  0 a*X a^3*X a^3*X a^2*X a^5*X  X a^3*X 2*X  0 a^5*X a*X a^2*X  X a^5*X 2*X a^6*X a^6*X a^6*X a^6*X  0 a^3*X a^3*X 2*X a^6*X a^6*X a^7*X  0  X a*X  X a^6*X a^2*X 2*X a^3*X a^2*X a^7*X  0
 0  0  X a^7*X a*X a^2*X a^6*X a^7*X a^3*X a^6*X 2*X a*X 2*X a^2*X  0  0 a^6*X 2*X a^2*X a^6*X a^7*X a^5*X a^5*X a^3*X a^5*X 2*X  0 a^5*X a*X a^7*X a^2*X a^3*X 2*X a^6*X a^7*X a^5*X a*X a^3*X a*X a^2*X a^3*X a^3*X a^6*X a^2*X a*X 2*X a^2*X a^5*X a*X 2*X a^3*X a^7*X a^6*X  X a^7*X  0

generates a code of length 56 over F9[X]/(X^2) who´s minimum homogenous weight is 432.

Homogenous weight enumerator: w(x)=1x^0+64x^432+312x^441+5832x^448+216x^450+72x^459+16x^477+40x^486+8x^504

The gray image is a linear code over GF(9) with n=504, k=4 and d=432.
This code was found by Heurico 1.16 in 0.0342 seconds.