The generator matrix 1 0 0 1 1 1 0 1 1 1 1 0 2 0 1 1 1 1 2 0 2 1 0 1 1 2 0 1 1 1 2 0 2 1 1 1 1 1 2 1 0 2 1 0 1 2 2 0 2 1 0 1 1 1 1 1 2 0 1 1 0 1 1 1 1 2 0 2 0 2 1 0 1 2 1 1 1 2 1 0 1 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 2 3 1 0 2 1 0 1 0 0 1 2 1 1 3 2 2 2 1 1 0 1 0 1 3 1 3 1 2 3 1 1 2 1 1 1 1 1 2 1 2 0 2 1 0 0 3 1 0 3 2 0 0 1 1 1 2 3 1 2 1 0 1 2 1 2 1 3 1 0 0 0 0 1 1 1 0 1 0 1 1 0 2 3 1 0 3 0 1 1 1 2 1 1 1 0 3 0 0 3 2 1 1 2 0 1 0 3 0 3 2 3 1 1 1 0 1 1 2 3 2 2 3 2 0 1 1 1 1 1 1 2 2 1 2 3 1 3 2 1 1 2 2 0 1 3 3 1 0 3 2 2 1 0 0 0 0 0 2 0 0 0 0 0 0 0 2 2 0 2 2 2 2 2 0 0 2 0 0 2 2 2 2 2 2 0 2 0 2 2 0 2 0 2 2 2 2 0 0 2 0 0 0 2 2 2 0 2 2 2 0 0 2 2 0 0 0 0 2 2 0 2 0 0 2 0 0 0 0 2 2 2 0 2 2 0 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 2 2 2 0 2 2 0 0 2 2 2 0 0 0 2 0 0 2 2 2 2 0 2 0 0 0 0 0 2 2 0 0 2 2 2 2 2 0 2 2 2 0 2 0 0 0 0 0 2 2 0 0 2 0 0 2 0 0 0 2 0 0 0 0 2 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 2 2 2 2 2 2 2 0 2 0 0 2 0 2 0 2 0 0 2 2 0 2 0 2 2 2 2 2 0 0 2 2 0 2 2 0 2 2 2 2 0 0 0 0 0 2 2 2 0 0 0 2 2 0 0 0 2 2 0 2 0 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 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 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 2 2 2 2 0 2 2 0 2 0 2 2 2 2 0 2 0 2 2 0 2 0 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 2 2 0 0 0 2 0 0 2 0 0 0 2 2 2 2 2 2 0 0 2 2 2 2 2 2 0 0 0 0 2 2 2 2 0 0 2 2 0 2 0 0 0 2 0 0 0 2 0 2 0 2 0 2 2 0 2 2 2 0 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 2 2 2 0 2 2 2 0 0 0 0 0 2 2 0 2 2 2 0 2 0 0 0 0 2 2 0 0 2 0 0 2 0 2 0 2 0 0 2 2 2 0 0 0 2 2 0 0 0 2 0 2 0 0 2 0 2 2 0 2 2 2 0 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 2 0 2 2 0 2 0 2 2 2 0 0 2 0 2 2 2 0 2 0 0 2 2 0 0 0 2 0 0 2 2 2 2 2 2 0 0 2 2 0 0 0 0 2 2 0 0 2 2 0 2 0 2 2 0 0 0 0 0 0 0 0 0 0 2 0 0 2 2 2 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 2 2 2 0 0 0 2 2 0 2 2 2 2 0 0 2 0 2 2 2 2 0 0 0 2 2 2 0 0 2 2 0 2 0 0 2 2 2 0 0 2 2 2 0 0 0 0 0 2 0 2 0 2 0 2 0 0 0 0 2 0 0 2 0 0 generates a code of length 84 over Z4 who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+122x^68+148x^70+515x^72+556x^74+1159x^76+1106x^78+1848x^80+1694x^82+2084x^84+1826x^86+1719x^88+1250x^90+1092x^92+454x^94+468x^96+114x^98+142x^100+18x^102+54x^104+2x^106+9x^108+3x^112 The gray image is a code over GF(2) with n=168, k=14 and d=68. This code was found by Heurico 1.16 in 54 seconds.