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 2 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 2 0 0 0 2 2 2 2a 0 2 2a 2a 2a 2a 2 2a 2a^2+2a+2 0 0 2 2a^2+2a 2a^2 2a^2+2a 2a^2 2a+2 2a^2 2a^2+2 2 2a+2 2a^2+2a 2a 0 2a 2a^2+2a 2a^2 2a+2 2a^2+2a 2a^2+2a+2 2 2a^2+2 2 2a 2a^2+2a+2 2a 2a^2 2 2a^2+2 2a^2+2a+2 2a 2a^2+2a 2 2 2a^2+2a+2 2a 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^2 2a 0 2a 2a^2+2a+2 2a^2 2a+2 2a^2+2a 2a+2 2a^2+2a+2 2a^2+2 2a^2+2a+2 2a^2+2 2a^2+2 2a 2a^2+2a 2a^2+2a+2 2a 2a 2a^2+2a 2a^2+2a 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^2+2a+2 2 2a^2+2a+2 0 2a^2+2 2a^2+2a+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 2 2a^2+2a 2a 0 2 2 2a^2+2a+2 2a^2+2a+2 2a 0 2 2a^2+2a+2 0 2a^2 2 2a+2 2a^2+2a+2 2a+2 2a^2+2a+2 2 2a^2 2 2a 2 0 2a^2+2 2a^2+2 0 2 0 2a 2a^2+2a 2a^2+2a 2a^2+2 2a 2a^2+2a+2 2a^2+2a 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 2a^2+2a 2 2a+2 2a 2a+2 0 2a^2+2 2a^2+2a 2 0 2a^2 2a^2+2 2 2a^2+2a 2 2a^2 2a^2 2a^2+2a 2a 2 2a+2 2a^2+2 2a^2+2a+2 2a^2 2a 2a^2 2a 2a^2+2a 2a^2+2a 2 2a^2+2 2a+2 2 2a^2+2a+2 2a^2+2 2a^2 0 0 generates a code of length 56 over GR(64,4) who´s minimum homogenous weight is 344. Homogenous weight enumerator: w(x)=1x^0+189x^344+980x^352+1967x^360+2842x^368+3472x^376+3584x^378+4270x^384+50176x^386+4473x^392+175616x^394+4592x^400+4235x^408+3227x^416+1778x^424+616x^432+126x^440 The gray image is a code over GF(8) with n=448, k=6 and d=344. This code was found by Heurico 1.16 in 34.8 seconds.