The generator matrix 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2a^2+2 1 2 1 1 2a^2+2a+2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2a^2+2a 1 1 1 1 2a^2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 0 1 0 2a^2+2 2a 2a^2+2a 2 2a^2+2a+2 2a+2 2a^2 1 2a^2+a+2 a^2 2a^2+3 2a^2+3a+2 3a^2+2 3a^2+3a+1 3 2a^2+3a a^2+3a+3 a^2+2 1 a^2+a+1 1 a+2 2a^2+1 1 3a^2+1 3a^2+2a+1 2a^2+3a+1 a^2+3 2a^2+a+3 3a+1 a^2+2a+3 2a+1 3a^2+3a+3 3a^2+2a+2 3a^2+3 3a^2+a+1 a+1 a^2+3 1 3a+3 3a a^2+2a a^2+3a+3 1 2a^2+2a+1 a^2+3a+2 a^2+a a^2+3a a^2+a+2 3a^2+a a^2+a+3 3a^2+a+2 2a^2+a+2 a^2+a 2a^2+a+1 a^2 3a+3 3a^2+1 1 3a^2+3a+2 2a^2+2 0 0 1 1 a a^2 3a+3 a^2+3a a^2+3a+3 a^2+2a+1 a^2+2a+3 3a^2+2a+1 a^2+1 a^2+3a+1 2a^2+3 2a^2+a+1 a^2+2a 3a^2+2a+2 3a^2+3a+2 a+2 a^2+a+2 2a+1 a^2+a+3 a+1 3a+1 3a 3a^2+3a+3 3a^2+a+1 2a^2+3a+3 2a^2+a+3 2a+1 2a+3 3a^2+3a+3 2a^2+2a 2a+2 3a^2+2a+3 2a^2+3a+2 a^2+2a a+1 a^2+2a+2 3a^2+3a a^2+3a a^2+3a 3a 3a^2+2a+2 2a^2 3a^2+2a+1 3a^2+3a 2a 3a^2+a+2 3a^2+2a+1 3a^2+a+1 2a+3 2a^2+3 3a^2+2a 2a+2 3a+3 a 3a^2+3a+1 0 a^2+2a+1 3a^2+2a 2 2a^2+2a generates a code of length 64 over GR(64,4) who´s minimum homogenous weight is 431. Homogenous weight enumerator: w(x)=1x^0+1960x^431+6678x^432+6104x^433+840x^434+336x^436+16464x^439+31591x^440+16296x^441+3304x^442+1120x^444+20776x^447+35567x^448+17640x^449+4312x^450+2128x^452+28896x^455+44933x^456+20888x^457+2296x^458+7x^480+7x^496 The gray image is a code over GF(8) with n=512, k=6 and d=431. This code was found by Heurico 1.16 in 12.6 seconds.