The generator matrix 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 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 1 2 1 1 1 1 1 1 1 2 1 1 2a^2+2 1 2 1 1 1 0 1 1 a 3a^2+2 2a^2+3a+1 a^2+3a a^2+3a+3 3a^2+2a+3 a 3a^2+2 a^2+3a 1 0 2a^2+3a+1 3a^2+2a+3 2a^2+3 a^2+3a+3 3a^2+2a+3 a 1 a^2+3a 0 3a^2+2 a^2+3a+3 2a^2+3a+3 3a^2+2a+2 2a^2+3a+1 2 a^2+3a+1 a^2+a a+2 3a^2+2a+2 a^2+a a^2+a+3 2a^2+3a+3 2a^2+a+3 2a 2a^2+2 2a^2+a+3 2a+2 1 2a^2+2a+2 3a^2+3a+1 2a^2+3 3a^2+3a a^2+a 2a+2 2a^2+3a+3 2a^2+a+1 3a^2+3 a+2 1 a+1 2a^2+2 3a^2+3 2a^2+a 2a^2+3 a^2+3 2a^2+a+3 1 a^2+2a 2a^2+2 1 3a^2+3 1 3a^2+a+3 2a^2+a+1 3a^2+2 0 0 2a^2+2 0 2 2 2a+2 2 2a^2 2a+2 2a^2+2 2a^2 2 2a^2+2a 2a^2+2a+2 0 2a^2+2 2 2a^2+2a+2 2a 2a 2a^2+2a 2a+2 2 2a^2+2a+2 2a^2+2 2a^2+2a+2 2a^2 2a^2+2a 2a^2+2a 2a^2+2a 2a^2 2a^2+2 2a^2 2a^2+2a+2 2 2a^2+2a+2 0 2a^2+2 2a^2+2a 0 2a 2a+2 2a 0 2a 2a^2+2a+2 2a^2 2a^2+2a+2 2a+2 2a+2 2a^2 0 2a+2 2a^2+2 2a^2 0 0 2a^2+2a+2 2a^2+2 2a 2a^2+2 2a^2 2a^2+2a+2 0 2a^2+2a 2a^2+2a 2a+2 2a^2+2a+2 0 0 0 2 2a^2+2 2a^2+2a+2 2a+2 2a^2 2a^2+2a+2 2a^2+2 2a^2+2 2a^2+2 2a^2+2a+2 2a+2 2a+2 2a^2 2a^2 2a 2a^2 2 0 2a^2+2a 2a 2 2a 2a^2+2a 2a^2+2 2a+2 0 2 2a^2+2a+2 2a 2a 2a+2 0 2a 2a^2+2a 2a^2+2a+2 0 2a+2 2a^2+2a 2a^2 2a^2+2a+2 0 2a^2+2a 2a^2+2a 0 2a^2+2a 2a 2a^2+2 2a^2 2a^2+2 2a^2+2 0 2a+2 2a^2+2a 2a+2 2a 2a^2+2 2a^2 2a+2 2a+2 2a^2 2a^2+2a+2 0 2a+2 2a^2+2 2a^2 2a^2+2a+2 generates a code of length 69 over GR(64,4) who´s minimum homogenous weight is 456. Homogenous weight enumerator: w(x)=1x^0+350x^456+448x^458+168x^459+1120x^462+2128x^463+756x^464+1120x^465+6048x^466+2352x^467+4200x^470+5936x^471+763x^472+3360x^473+16800x^474+4480x^475+5320x^478+16016x^479+644x^480+11424x^481+46816x^482+11984x^483+11704x^486+27664x^487+378x^488+12768x^489+44576x^490+9688x^491+6328x^494+5600x^495+364x^496+266x^504+196x^512+175x^520+98x^528+77x^536+21x^544+7x^552 The gray image is a code over GF(8) with n=552, k=6 and d=456. This code was found by Heurico 1.16 in 16.4 seconds.