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  3  1  1  1  1  1  1  1  1  1 3a+3  3 3a  1  1  1  1  1  1  1  1 3a+3  1  1  1  1  1  1 3a  1  1  1  1  1  1  1  1 3a+3 3a  1  1  1
 0  1  1  a 7a+7 8a+4 3a+5 8a+5 8a a+5  0 a+5 8a  a 8a+5 3a+7 7a+7 8a+4  1 3a+5  0 3a+7 8a+5 8a+4  1  a 3a+5 7a+7  3 8a a+5 2a+5 a+8 6a+5 2a+5  1 a+3 6a+8 4a+8 4a+3 8a+7 6a+5 2a+4 8a+3 4a+5  1  1  1 a+7 a+3 7a+8 3a+7 a+3 6a+5 2a 7a+6  1 8a+1 a+5 4a+2 3a+2 4a+3 8a+3  1 6a+5 7a+8 5a+2 4a+8 a+7 2a+5 2a+7  5  1  1 6a+7 2a+2 a+5
 0  0 3a+6  0 3a+6  3 6a+6 6a+6  6 3a 3a+6 3a  3  0 6a 6a+3 6a+6  6 6a 3a 6a  6 3a 6a+3 6a 3a+3 3a+6  0 6a  6  3 6a 6a+3  0 6a+6 6a+3  3  6  3 3a  6  3 3a 3a+6 3a+6 6a+3  6 3a 6a  0  3 3a+6 3a+3 6a 6a+3  3  0 3a+3 3a+6  6 6a 6a+6  0 3a+3  0  6 3a+3 3a 6a+6  6  3 6a+6 3a+3  6 3a+3 3a  6
 0  0  0  3 3a+6 3a+6  3 3a  3 3a+3 6a 6a+6 6a 3a 3a+3 3a+6  0 6a+3 3a 6a+3 6a+6  6 3a 6a  3  0  3 3a+6 3a 6a+6 3a  6 3a 6a+6 6a+3  0 6a+3 3a+3 6a  3 6a+6 6a+3 6a  0 6a 3a  6 3a+3  3  6  3  6  6 6a 6a+3 3a 6a+6 6a+6 6a+6  6 6a+3 6a  3 6a  0 3a+6 6a+3 6a 3a 3a+3  3 3a+6 3a+6 6a+6  0 6a+6 6a+3

generates a code of length 77 over GR(81,9) 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 code over GF(9) with n=693, k=6 and d=583.
This code was found by Heurico 1.16 in 44.3 seconds.