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 2 1 1 1 1 2 2 2 2 2 2 2 2 2 0 1 2 1 1 1 2 2 0 1 2 0 1 2 1 1 1 1 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 2 2 0 2 2 0 0 0 0 0 0 0 2 2 2 0 0 2 2 0 2 2 0 0 2 2 0 0 0 2 2 2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 0 0 0 0 0 2 0 2 2 0 2 2 2 0 0 2 2 2 0 2 0 0 0 2 2 2 0 2 2 2 2 0 2 2 2 2 2 2 2 0 0 0 0 2 2 2 0 2 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 2 2 2 2 2 2 0 0 0 2 0 2 2 2 0 2 2 0 0 2 2 0 2 2 2 0 0 2 0 0 0 0 0 2 0 0 2 2 2 0 0 0 2 0 2 2 0 2 2 0 0 0 2 0 0 2 0 0 2 2 2 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 2 2 2 2 2 2 0 0 0 0 2 0 2 2 0 0 2 0 2 2 2 2 2 0 0 0 2 0 2 0 0 0 2 2 0 2 2 2 0 2 0 2 0 2 0 0 0 2 2 0 2 2 2 0 0 0 2 0 0 0 2 0 0 2 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 2 2 2 2 2 2 0 2 2 0 2 2 2 0 0 0 2 2 2 2 0 2 2 0 2 0 0 0 0 2 0 0 0 0 2 0 2 0 0 0 2 2 0 0 2 0 0 2 0 0 0 2 2 2 2 0 0 2 2 2 2 2 0 0 2 2 2 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 2 0 0 2 2 0 2 2 0 2 0 2 0 2 2 2 2 0 0 0 2 0 2 0 0 2 2 0 0 2 0 0 2 2 2 2 2 2 2 0 2 0 0 2 0 2 0 0 0 2 0 2 2 0 0 0 0 0 2 2 2 2 0 2 0 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 2 2 2 2 0 2 2 0 2 0 2 0 0 2 0 0 0 0 2 0 2 2 0 2 2 2 0 0 2 2 0 2 0 0 0 0 0 2 2 2 2 0 0 2 2 2 2 2 2 2 2 0 2 0 2 0 2 0 2 2 0 2 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 2 0 0 0 0 2 2 0 2 0 0 0 2 2 2 0 0 2 0 2 2 0 2 2 0 0 0 2 2 2 2 0 0 2 2 2 2 2 0 0 2 2 2 2 0 0 2 0 2 0 0 0 2 0 0 0 0 0 0 2 0 0 2 2 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 0 2 0 0 2 0 2 0 0 2 0 0 0 0 2 2 2 0 0 2 2 0 0 2 2 2 2 0 2 2 0 0 2 2 0 0 0 0 0 2 2 2 0 2 0 0 2 2 0 2 2 0 0 0 2 0 2 2 0 2 0 0 2 2 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 2 2 2 0 0 0 2 0 0 2 2 0 0 2 0 2 2 0 0 2 2 0 0 0 2 0 2 2 0 0 0 2 2 2 0 0 0 2 0 0 2 0 0 0 2 0 0 0 0 2 2 0 2 0 2 0 2 0 0 0 2 2 0 2 0 2 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 0 0 2 2 2 2 2 0 2 0 2 0 0 0 0 0 2 2 2 2 2 0 0 2 0 2 0 0 0 0 0 2 2 2 2 2 0 0 2 2 0 2 0 2 2 0 0 2 2 2 0 0 0 0 2 2 2 2 2 0 0 0 2 2 0 2 0 0 2 2 generates a code of length 86 over Z4 who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+125x^68+346x^72+12x^74+520x^76+122x^78+825x^80+530x^82+1273x^84+740x^86+1280x^88+496x^90+818x^92+130x^94+507x^96+18x^98+267x^100+129x^104+34x^108+15x^112+3x^116+1x^136 The gray image is a code over GF(2) with n=172, k=13 and d=68. This code was found by Heurico 1.16 in 45 seconds.