The generator matrix

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

generates a code of length 80 over F9[X]/(X^2) who´s minimum homogenous weight is 623.

Homogenous weight enumerator: w(x)=1x^0+1008x^623+2160x^628+3024x^629+6328x^630+6336x^632+3456x^637+3024x^638+3632x^639+3744x^641+6048x^646+5616x^647+8184x^648+6408x^650+48x^657+16x^666+8x^675+8x^711

The gray image is a linear code over GF(9) with n=720, k=5 and d=623.
This code was found by Heurico 1.16 in 8.66 seconds.