The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 1 2a^2+2 1 1 1 1 1 1 1 1 1 1 1 1 2a^2+2a 1 1 1 1 1 1 2a 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2a^2+2a 2a^2+2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2a+2 2a 0 2a+2 1 1 1 1 0 1 1 1 1 1 0 1 0 1 a a^2 3a+3 a^2+3a a^2+3a+3 a^2+2a+1 2a^2+2 2a^2+3 a+2 a^2+2 1 3a^2+3a+1 2 2a^2+2a+3 a+3 3a^2+2 3a^2+3a 3a^2+3 2a^2+a+2 2a^2+3a+1 a^2+3 3a^2+3a+2 3a^2+3a+3 1 2a+3 a^2+2a+2 2a 2a^2+3a 3a+1 a^2+3a+2 1 3a^2+a a^2+a+3 a^2+3a a^2+2a+3 3a+3 3a 3a^2+a+1 3a^2+a+3 a^2+3 0 2a^2+a+1 2a^2+2a+2 2 2a^2+2a+1 3a^2+2a+3 a^2+a+1 a^2+1 1 1 2a^2+3a 2a^2+a 2a^2+2a+2 2a^2+2 3a^2+2a+1 a+1 2a^2+2a+3 3a^2+2a a^2 1 a^2+3a+1 2a^2+a+2 3a^2+3 2a^2+a+3 2a^2+3 2a^2 a^2+3a+2 3a^2+a+3 1 1 1 1 2a^2+3a+1 a^2+3a+1 3a^2+2a+3 2a^2+2a+2 1 3a+1 a^2+2a a^2+2a+2 a^2+2a 2a^2+2a+2 0 0 1 a^2+2a+1 a 3a^2+3a+2 1 a^2+3a+3 2a^2+3a+1 a^2 3 a^2+a+3 2a^2+2 3a^2+2 a^2+2a+3 2a^2+2a+1 a+3 2a^2+a 3a^2+2a+1 2a 3a^2+3 a^2+3a+1 3a^2+a+2 3a a+1 a^2+3a+2 3a^2 2a^2+3a 2a^2+3 a^2+1 3a+2 a^2+2a 3a^2+3a+1 3a+1 a+3 a^2+a+2 3a^2+a 2a^2+2a+2 3a a^2+a+2 a 2a^2+3a 3a^2+2a+2 a^2+a+3 3a^2+2a 2a+2 1 2a^2+3a+3 3a^2+1 3a^2+3 a^2+3 3a+3 2 2a+1 2a^2+a+3 2a^2+2 a^2+3a+3 2a^2+1 a^2+a+3 a^2+a+1 a^2 2a^2+3a 2a^2+a+1 2a^2+2a+2 2a^2 a^2+2a a^2+2a+3 2 3a+2 a^2+a+1 a^2+2a 2a^2+1 a^2+3 0 2a^2+a+2 3a^2+a+1 a^2+3 3a^2+3a a^2+3a a^2+2a+2 2a^2+a+3 2a^2+a+1 3a^2+a+2 3a^2+a+3 2a^2+3a+2 1 generates a code of length 86 over GR(64,4) who´s minimum homogenous weight is 582. Homogenous weight enumerator: w(x)=1x^0+2968x^582+3360x^583+889x^584+672x^585+1176x^586+1064x^587+3136x^588+6272x^589+14672x^590+11256x^591+1834x^592+3528x^593+4144x^594+4256x^595+5152x^596+10136x^597+21000x^598+16744x^599+5110x^600+6608x^601+6104x^602+4424x^603+7168x^604+10192x^605+20384x^606+18312x^607+6874x^608+7112x^609+6496x^610+4592x^611+6048x^612+9240x^613+19824x^614+11256x^615+28x^616+35x^624+35x^632+28x^640+14x^648 The gray image is a code over GF(8) with n=688, k=6 and d=582. This code was found by Heurico 1.16 in 17.8 seconds.