The generator matrix 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 2 0 0 2 2 2a 2a^2 2a^2+2a 2a^2+2a+2 2a^2+2a+2 2 2a^2+2a+2 2a^2+2 0 2a 2a^2+2a+2 2a 2a^2+2a+2 0 2a^2+2a 2a 2a 2a^2 2a 2 2a^2+2a 2a^2 2 2a+2 2a^2+2 2a^2+2a 0 0 2a^2+2a 2a^2 2a^2 2a^2+2 2a^2 2a+2 2a^2 2a^2+2a+2 2a^2 2a^2+2a+2 2a^2+2 2a^2+2a 2a 2a^2+2a 2 2a^2+2a 2 2a^2+2a+2 2a 2 2 2a^2+2a+2 2a^2 2a^2 2a+2 2a^2+2a 2a^2+2a 2a^2+2a 0 2a^2 2a^2+2 2a^2+2 2a^2 2a^2+2a+2 2a^2+2 0 2a^2+2a+2 2a 2a 2a 2 0 0 2 2a^2 0 0 2a+2 0 2a^2+2a 2a^2+2a+2 0 0 2 0 2a^2+2 2a^2+2a+2 2a 2a^2+2 2a^2+2 2a 2a^2+2 2a^2 2a 2a+2 2 2a^2+2a+2 2 2 2a^2+2a 2a+2 2 2a 2a^2+2a 0 2a^2 0 0 2a^2 2a^2 2a^2+2 2 2a^2+2a+2 2a^2+2a 2a^2+2 2 2a^2 0 2a^2+2 2a^2 2a^2+2a+2 2 2a^2 2a^2+2 2a^2+2a+2 2a^2+2a 2a^2+2a+2 2a^2+2a 2a 2a^2+2a+2 0 2a^2+2 2a^2 2 2a^2+2a+2 2a^2 2a^2+2a 2a^2+2a 2a^2+2a 2a+2 2a 2a^2 2a^2+2a+2 2a+2 2a^2+2a 2a^2+2a+2 2a+2 2a^2+2a+2 2a+2 2a^2+2a 2a 2a 2a^2 2 2a 2a 0 2 0 2a^2+2a+2 2a 0 2a^2 2a^2+2 2a^2+2 2a+2 0 0 0 2 2 2a^2+2a 2a^2+2a 2 2a^2+2 2a^2+2a 2a^2+2 2a^2+2 2a+2 2a 2a^2+2a 2a 2a+2 2a^2+2a+2 2a^2+2 2a^2 2a^2+2a 2 0 2a^2+2a+2 0 2a^2+2a+2 2a 2a^2+2 2a+2 0 2a+2 2a^2+2 2a+2 2a^2+2a 2a^2 2a 0 2a^2+2a 2a^2 2 2a^2 2a+2 0 2a^2+2a+2 2a+2 2a^2+2a+2 2a^2 2a^2+2a+2 2a+2 2a^2+2a 2a^2+2 0 2a^2 2a^2 2a^2+2a+2 2a^2+2a 2a^2+2 2a^2+2a+2 2a^2 2a^2+2 2 2 0 2a 2a+2 2a^2+2 2a^2+2a 2 0 2a+2 2 2a^2+2 0 2a^2+2 2a+2 2a+2 2 2a+2 2a^2+2a+2 2a 2a^2 2a+2 0 2a^2+2a+2 2a^2 generates a code of length 85 over GR(64,4) who´s minimum homogenous weight is 568. Homogenous weight enumerator: w(x)=1x^0+518x^568+679x^576+714x^584+602x^592+28672x^595+392x^600+343x^608+273x^616+147x^624+147x^632+77x^640+112x^648+63x^656+21x^664+7x^680 The gray image is a code over GF(8) with n=680, k=5 and d=568. This code was found by Heurico 1.16 in 0.968 seconds.