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

generates a code of length 56 over F9[X]/(X^2) who´s minimum homogenous weight is 414.

Homogenous weight enumerator: w(x)=1x^0+216x^414+944x^423+1752x^432+11432x^441+42312x^450+864x^459+504x^468+536x^477+368x^486+112x^495+8x^504

The gray image is a linear code over GF(9) with n=504, k=5 and d=414.
This code was found by Heurico 1.16 in 1.15 seconds.