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 2 2 2 2 2 2 2 2 1 2 2 1 0 2 0 1 1 0 1 0 1 1 1 1 2 0 1 1 2 1 1 2 1 2 1 1 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 2 2 2 2 0 2 0 0 0 2 2 2 0 2 2 2 0 0 2 0 2 2 0 0 2 0 2 2 0 2 0 0 0 2 2 2 2 0 2 2 2 2 0 0 2 0 0 2 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 0 0 2 2 2 0 0 0 2 2 2 0 2 2 0 0 2 2 2 2 0 0 0 0 0 2 0 0 0 2 0 2 2 2 0 0 2 0 0 2 2 2 2 2 0 0 2 0 2 2 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 2 0 2 0 0 2 2 0 0 0 2 2 2 0 2 0 2 2 0 2 2 2 0 2 2 2 0 2 0 0 0 2 0 2 0 2 0 0 2 0 0 2 0 2 0 0 0 0 0 0 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 2 0 2 2 0 0 0 2 0 0 0 0 2 0 0 0 0 0 2 2 0 2 0 0 0 0 0 0 2 0 2 2 2 0 2 2 2 2 0 2 2 2 2 2 2 0 2 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 2 2 0 0 0 2 0 2 0 0 0 0 2 2 0 2 2 2 2 2 0 0 0 0 2 0 2 0 2 2 0 0 2 0 0 0 0 0 2 2 2 2 2 0 2 0 2 2 0 2 2 2 2 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 2 2 2 0 0 0 0 2 0 0 0 2 2 2 2 0 2 0 0 0 2 0 2 2 0 0 2 0 0 0 2 2 0 2 0 0 2 2 0 2 2 0 0 0 2 2 2 0 0 0 2 2 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 2 2 0 0 0 2 2 2 2 2 0 0 0 0 2 2 2 2 2 0 2 2 0 2 2 0 2 0 2 0 2 2 0 2 2 2 0 2 0 2 0 2 2 2 0 0 0 2 2 2 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 2 2 2 2 0 0 0 2 2 2 2 0 2 0 2 2 2 2 2 2 2 2 2 2 0 2 2 2 0 0 0 2 0 2 0 2 2 2 0 0 2 0 2 0 2 2 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 2 2 0 0 0 0 2 0 0 0 2 0 2 0 2 2 2 0 0 2 0 0 0 2 0 0 2 2 0 2 0 2 0 2 0 0 0 2 2 0 2 2 2 2 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 0 2 0 0 2 0 2 2 0 0 0 2 0 0 2 0 0 2 0 0 2 2 2 0 2 2 2 0 2 2 0 0 2 2 2 0 2 2 0 2 2 0 0 2 2 2 0 0 2 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+64x^68+245x^72+30x^74+399x^76+164x^78+535x^80+310x^82+679x^84+344x^86+501x^88+138x^90+321x^92+36x^94+179x^96+2x^98+93x^100+42x^104+12x^108+1x^128 The gray image is a code over GF(2) with n=168, k=12 and d=68. This code was found by Heurico 1.16 in 5.9 seconds.