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

generates a code of length 81 over F9[X]/(X^2) who´s minimum homogenous weight is 612.

Homogenous weight enumerator: w(x)=1x^0+192x^612+72x^614+72x^619+360x^620+1792x^621+792x^622+1368x^623+720x^626+1440x^627+2088x^628+9864x^629+9216x^630+4968x^631+5040x^632+4320x^635+5400x^636+6912x^637+22680x^638+18536x^639+9504x^640+11592x^641+18360x^644+19872x^645+20448x^646+63576x^647+43368x^648+21240x^649+20016x^650+29088x^653+25776x^654+22968x^655+60984x^656+36752x^657+15984x^658+14400x^659+424x^666+448x^675+288x^684+232x^693+152x^702+88x^711+32x^720+16x^729

The gray image is a linear code over GF(9) with n=729, k=6 and d=612.
This code was found by Heurico 1.16 in 48 seconds.