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 2 1 1 1 1 1 1 1 1 1 2 1 1 1 1 2 1 0 2 0 0 0 2 2 2 2a 0 2 2a 2a 2a 2a 2 2a 2a^2+2a+2 0 2 0 2a^2+2a 2a^2 2a+2 2a^2+2a+2 2a+2 2a^2 2a+2 2a^2+2a+2 2a 2a^2+2a+2 2a 2a^2+2a 2a^2+2 2a^2+2a+2 2a^2+2a+2 2 2 2a^2+2 0 2a^2+2a 2a 2a^2+2 2a^2 0 2a 2a^2+2 0 2a^2+2a+2 2a^2 2a 2a^2+2 2 2a^2+2 2a^2+2a 2 2a^2 0 2 0 2a^2+2a 2a^2+2a 2 2a^2+2a+2 2a^2 2 2a^2+2 2a 2 2a^2+2a 2 0 0 0 2 0 0 2a^2+2 2a^2+2a+2 2a^2+2a 2a^2+2a 2 2a+2 2a^2+2 0 2 2a^2+2a+2 2a^2 2a 2a^2+2 2a 0 2a^2 2a 2a^2+2a+2 2a^2+2a 2a+2 2a^2 2 2a^2+2a+2 2 2a^2+2a+2 2a 2 2a+2 2a 2a^2 2a^2 0 2a^2 2a^2 2a^2 2a^2 2a^2+2a 2a^2 2a^2+2 2 2a^2+2a+2 2a^2+2 2 2a+2 0 2a^2 0 0 2a+2 0 2a 2a 2a^2+2a 2a 2a^2 2a+2 2a+2 2 2a^2 0 2a^2+2a 2 2 0 2a+2 2 0 0 0 0 2 0 2 2a^2+2a+2 2a 2a+2 2a^2 2a^2+2 0 2a^2+2a+2 2 2a 2a^2+2a 2a^2+2a 2a^2+2a 2a^2+2a 2a 2 0 2 2a+2 2a^2+2a 2a^2+2 2a^2+2a 2 2a^2+2a 2a 0 0 2a^2 2a 2a^2 2a+2 2a 2a+2 2 0 2a^2 2a^2+2a 2a^2+2 0 2a 2a^2+2a 2a 2a^2+2 0 2a^2 2a^2+2a 0 2a+2 2 2a^2+2a 2a+2 2 2a 2a^2+2a 2 2a^2 2a^2+2 2a+2 2a+2 2a^2+2a+2 2a 2a^2+2a+2 2a+2 2a^2+2a+2 2a^2+2a+2 2 0 0 0 0 0 2 2a^2+2 2a+2 2a 2a^2+2a+2 2a 2a^2 2a^2 2a+2 0 2a 0 2a^2 2a^2+2a 2 2a+2 2a^2+2a 2a 2a+2 2a 2 2a^2+2a+2 0 2a^2+2a+2 2a^2+2a+2 2 2a^2+2a 0 2a^2+2a+2 2a^2+2a+2 2a+2 0 0 2 2a 2a+2 2a 2a^2+2 2a^2+2 2 2a+2 2 2a+2 2a^2+2 2a^2+2a+2 2 2a^2+2a 2a 2 2a+2 0 2 2a^2+2a 2 2a^2 2a 2 2 2a^2+2 2a+2 2a^2+2 0 2a^2 2a 2a 2a^2+2a+2 2a 2a^2+2a+2 generates a code of length 72 over GR(64,4) who´s minimum homogenous weight is 456. Homogenous weight enumerator: w(x)=1x^0+329x^456+1421x^464+2317x^472+2961x^480+448x^483+3318x^488+9408x^491+3675x^496+65856x^499+4102x^504+153664x^507+4207x^512+3801x^520+2954x^528+2016x^536+1225x^544+350x^552+84x^560+7x^568 The gray image is a code over GF(8) with n=576, k=6 and d=456. This code was found by Heurico 1.16 in 47.1 seconds.