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

generates a code of length 78 over F9[X]/(X^2) who´s minimum homogenous weight is 621.

Homogenous weight enumerator: w(x)=1x^0+496x^621+5832x^624+216x^630+8x^648+8x^702

The gray image is a linear code over GF(9) with n=702, k=4 and d=621.
This code was found by Heurico 1.16 in 0.0851 seconds.