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

generates a code of length 82 over F9[X]/(X^2) who´s minimum homogenous weight is 621.

Homogenous weight enumerator: w(x)=1x^0+232x^621+1040x^630+1320x^639+6792x^648+47344x^657+640x^666+432x^675+368x^684+376x^693+264x^702+152x^711+64x^720+16x^729+8x^738

The gray image is a linear code over GF(9) with n=738, k=5 and d=621.
This code was found by Heurico 1.16 in 1.8 seconds.