The generator matrix 1 0 1 1 1 0 1 1 0 1 1 0 1 1 2 1 1 0 1 1 0 1 1 2 1 1 1 0 0 1 1 1 1 1 0 0 2 1 1 1 1 0 1 1 1 0 1 0 1 2 1 1 1 1 2 0 1 1 1 1 0 1 1 2 1 2 1 1 0 1 1 2 1 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 1 0 1 1 0 1 1 2 3 1 0 3 1 0 3 1 2 3 1 0 3 3 1 1 0 3 1 0 2 1 1 1 3 0 0 3 1 1 0 3 1 1 1 0 1 2 1 2 3 1 1 0 1 3 3 1 1 0 1 0 1 2 3 2 1 3 2 2 1 3 0 1 2 0 1 3 0 0 1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 2 0 2 0 2 2 2 0 0 2 2 0 2 2 2 2 2 0 0 2 0 0 2 2 0 0 0 0 0 2 0 0 0 2 2 2 0 2 0 2 2 2 0 0 0 0 0 2 0 2 0 0 2 0 2 0 2 2 0 2 2 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 0 0 2 2 0 0 0 2 0 2 0 2 0 0 2 2 0 0 2 0 2 0 2 2 2 0 2 2 0 2 2 2 2 0 0 2 0 2 2 0 0 0 2 0 2 2 0 2 2 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 2 2 2 2 0 2 0 2 2 0 2 0 2 0 2 0 2 0 0 0 0 2 2 2 0 2 0 0 2 0 2 0 2 0 0 2 0 0 2 2 0 2 2 0 2 2 0 0 0 2 0 2 0 0 2 0 2 0 0 2 0 2 2 2 0 2 2 2 0 0 0 0 0 2 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 2 2 0 0 0 2 0 2 2 0 2 2 0 2 2 2 2 0 2 2 0 2 0 0 2 2 2 0 0 0 2 0 2 2 0 2 0 0 0 0 2 0 2 0 2 0 0 0 2 2 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 2 0 0 2 0 0 2 2 2 2 2 2 0 0 2 0 2 2 2 0 2 2 0 0 2 2 2 0 0 2 0 2 0 2 0 0 2 2 0 0 2 2 2 2 0 0 2 0 0 0 0 0 2 2 0 0 0 2 2 2 2 0 2 2 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 2 0 2 0 2 2 2 2 0 2 0 2 2 2 2 0 2 0 0 2 0 2 0 0 2 0 0 0 0 2 2 2 0 0 0 2 0 0 0 2 0 2 2 2 2 0 0 0 2 0 2 2 2 2 0 2 0 2 0 2 2 2 2 2 0 0 2 2 0 0 2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 2 0 0 2 0 0 2 2 2 2 0 2 2 0 0 2 2 2 2 0 2 0 2 0 0 2 0 0 2 2 2 0 2 2 0 0 0 0 0 2 0 0 2 2 0 2 2 0 0 0 0 0 0 2 0 2 2 2 2 0 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 2 2 2 2 0 2 0 0 0 0 2 2 2 2 2 2 2 0 0 2 0 2 2 0 2 0 2 0 0 0 0 2 2 0 2 0 0 0 2 2 2 0 2 2 2 2 2 0 2 2 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 2 2 0 0 0 2 2 2 2 2 0 0 0 0 2 0 0 2 0 0 2 2 0 0 2 2 0 0 2 0 2 0 0 0 0 0 2 2 2 0 2 0 0 2 2 0 2 0 2 0 2 0 2 0 2 0 0 2 2 2 2 0 0 2 0 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 2 2 2 0 2 2 2 0 0 0 0 2 0 0 2 0 0 2 2 0 2 0 0 0 0 2 0 2 2 2 0 2 2 2 2 0 2 2 0 0 0 2 0 2 0 0 2 0 2 0 0 0 0 2 2 0 2 0 2 2 0 2 0 0 0 2 2 2 0 generates a code of length 84 over Z4 who´s minimum homogenous weight is 68. Homogenous weight enumerator: w(x)=1x^0+222x^68+44x^70+599x^72+416x^74+1254x^76+982x^78+1925x^80+1612x^82+2230x^84+1650x^86+1999x^88+1032x^90+1258x^92+330x^94+495x^96+76x^98+174x^100+2x^102+66x^104+12x^108+2x^112+2x^116+1x^128 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 94.6 seconds.