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

generates a code of length 53 over F9[X]/(X^2) who´s minimum homogenous weight is 396.

Homogenous weight enumerator: w(x)=1x^0+760x^396+72x^400+1120x^405+1728x^409+1152x^414+13824x^418+808x^423+36864x^427+912x^432+672x^441+552x^450+400x^459+168x^468+16x^477

The gray image is a linear code over GF(9) with n=477, k=5 and d=396.
This code was found by Heurico 1.16 in 1.14 seconds.