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 0 2 0 2 2a 2a 2a^2+2a+2 2a^2+2a+2 2a^2+2 2a^2+2 0 2 2a 2a^2 2a^2+2a+2 2a^2 0 2a^2 2a^2+2 2 2a^2+2 2a 2a^2 2a^2+2a+2 2a^2+2a 2a^2+2a 2a^2+2a 2a^2+2a 0 2 2a 0 2 2a 2a^2 2a^2+2a 2a^2+2a+2 2a^2+2 2a^2 2a^2+2a+2 2 2a^2+2a 2a^2+2 0 2a 2a^2 2a^2+2a 2a^2+2a+2 2a^2+2 0 2 2a 2a^2 2a^2+2a 2a^2+2a+2 2a^2+2 2a+2 0 0 2 2a^2+2 2a^2 2a^2+2a 2 2a^2 2a^2+2 2a^2+2a 2a 2a^2+2a 2a 2a 2a+2 2a+2 2a+2 2a^2+2 2a 2a+2 2 0 2a^2 2a^2+2a 2a^2+2 2a^2 2 0 2a^2 2a 2a^2+2 2a^2+2a 2 2a+2 2a^2+2a+2 2a^2+2a+2 2a^2+2a+2 2a^2+2a+2 2a^2+2a 0 2a^2+2a+2 2a 2a^2 2a^2+2a+2 2 0 2a^2+2a 2a^2+2 2a+2 2a^2+2 2a^2 2a^2+2a+2 2 2a+2 2a 0 0 generates a code of length 57 over GR(64,4) who´s minimum homogenous weight is 392. Homogenous weight enumerator: w(x)=1x^0+105x^392+3584x^399+392x^400+7x^448+7x^456 The gray image is a code over GF(8) with n=456, k=4 and d=392. This code was found by Heurico 1.16 in 0.0302 seconds.