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

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+120x^432+1728x^434+720x^435+1008x^436+4392x^437+2016x^438+280x^441+6912x^443+1800x^444+1872x^445+4824x^446+1152x^447+144x^450+14688x^452+3312x^453+2952x^454+8280x^455+2664x^456+64x^459+72x^468+16x^477+16x^486+8x^495+8x^504

The gray image is a linear code over GF(9) with n=504, k=5 and d=432.
This code was found by Heurico 1.16 in 0.388 seconds.