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  1  1  1  0  1  1  1  1  1  X  1  1  1  1  1  1 a*X  1  1  1  1  1  1  1  1 2*X  1  1  1  1  1  1 a*X  1  1  1  1  1  1 a*X a^2*X  1  1  1  1  1  1  1 2*X  1  1  1  1  1  1
 0  1  1  a a^7*X+a^2 a^3 a^7*X+2 a^7*X+a^6 a^5 a^7  0 a^7 a^5  a a^7*X+a^6 a^7*X+1 a^7*X+a^2 a^3 a^7*X+2  1  0 a^7*X+a^6 a^7 a^5 a^3  a a^7*X+2 a^7*X+a^2 a^7*X+1  X  1 X+a a^6*X+2 a^7*X+1 a^6*X+a^6 a^5*X+2  1 a^6*X+a^2 X+a^7 a^2*X X+a^5 X+a^3 a*X+a^5  1 X+a^3 a*X+a^7 2*X+a^6 a^2*X a^2*X+a a^3*X+a^3 a^6 a*X+a^5  1 a^5*X+a a^6*X+1 X+1 a^2*X a*X+a^7 a^6*X+a^7  1 a^2*X+a^6 X+a^3 2*X a^7*X+a^3 a^7*X+a^6 a^3*X+2  1  1 a^7*X+2 a^5*X+a^7 a^5*X+2 a^2*X+a^6 a^3*X+a^3 a*X+a^7 a^6*X+a^5  1 2*X+a^7 a^2*X+2 X+a^7 a*X+a^7 a^5*X+a^6  0
 0  0 a^7*X  0 a^7*X  X a^6*X a^6*X 2*X a*X a^7*X a*X  X  0 a^5*X a^3*X a^6*X 2*X a^3*X  0 a^5*X a^3*X a^5*X a^3*X 2*X a*X a^2*X a^5*X a^2*X  X a^6*X a*X a^7*X  0 a^3*X  X a*X  X 2*X  0 2*X a^6*X a^2*X a^6*X a^5*X a^7*X  0 a*X a^2*X a^2*X 2*X a^6*X  X a^3*X  0 a*X a^7*X 2*X a^6*X  0 a^2*X a*X a^3*X a^6*X a*X 2*X a^7*X  X a^2*X a^6*X a^5*X a^6*X  X a^2*X 2*X a^3*X a^7*X a^6*X a^7*X  X  X  X
 0  0  0  X a^7*X a^7*X  X a*X  X a^2*X a^5*X a^6*X a^5*X a*X a^2*X a^7*X  0 a^3*X a*X a^3*X a^6*X a^6*X 2*X a^3*X a*X  X  X a^5*X a^7*X  0  0 a^7*X a*X a^6*X 2*X a^5*X a^7*X a^2*X  X a^6*X a^2*X a*X  0 a*X  X a^6*X a^2*X a^3*X a^5*X 2*X a^3*X  0 a*X a^3*X 2*X a^6*X a^2*X 2*X a^2*X a^7*X a*X a^5*X  X a^2*X a^7*X a^2*X a*X a^5*X a^5*X a^6*X a^5*X  X  0 a*X  0  0 2*X a^6*X a^3*X a*X a^7*X a^7*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+248x^621+1368x^629+2672x^630+2232x^632+288x^633+2736x^635+2232x^636+11592x^638+11120x^639+5832x^641+3024x^642+11232x^644+6912x^645+27000x^647+20224x^648+11880x^650+16416x^651+39312x^653+20304x^654+63216x^656+42768x^657+19800x^659+32760x^660+51696x^662+23040x^663+54288x^665+32792x^666+12744x^668+440x^675+456x^684+280x^693+304x^702+160x^711+64x^720+8x^729

The gray image is a linear code over GF(9) with n=738, k=6 and d=621.
This code was found by Heurico 1.16 in 48.6 seconds.