The generator matrix

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

generates a code of length 77 over F9[X]/(X^2) who´s minimum homogenous weight is 583.

Homogenous weight enumerator: w(x)=1x^0+72x^583+656x^585+144x^588+432x^589+792x^590+1368x^591+1944x^592+288x^593+2648x^594+1440x^595+2520x^596+3168x^597+3888x^598+4896x^599+5688x^600+6336x^601+3024x^602+9720x^603+5400x^604+6048x^605+7776x^606+9072x^607+9720x^608+10368x^609+11376x^610+16416x^611+37480x^612+19872x^613+21168x^614+21024x^615+20952x^616+21024x^617+20880x^618+20088x^619+32760x^620+58976x^621+25776x^622+22752x^623+20376x^624+18144x^625+16056x^626+14184x^627+12672x^628+624x^630+480x^639+344x^648+240x^657+240x^666+80x^675+48x^684

The gray image is a linear code over GF(9) with n=693, k=6 and d=583.
This code was found by Heurico 1.16 in 45.9 seconds.