The generator matrix

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

generates a code of length 57 over F9[X]/(X^2) who´s minimum homogenous weight is 441.

Homogenous weight enumerator: w(x)=1x^0+48x^441+432x^442+2880x^443+2160x^444+4536x^445+336x^450+1728x^451+7200x^452+3456x^453+4536x^454+256x^459+3672x^460+13248x^461+6048x^462+8424x^463+48x^468+8x^477+16x^504+16x^513

The gray image is a linear code over GF(9) with n=513, k=5 and d=441.
This code was found by Heurico 1.16 in 0.412 seconds.