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  2  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  2  1  1  2  1  1  1  1  4  1  1  1  2  1  1  4  1  1  1  4  4  1  2  1  2  1  8  1  2  1  4  4  1
 0 12  0  0  0  4 12  4  8 12  8 12  0  4  8 12  0 12  4  8  0 12 12  0  0 12 12  4 12  4  0  0  8  8 12  4  8  0  4  0  8  4  0  0  4  0  4  8  4  8 12  4  8 12  8  4  4  4  0  0  4  0  0  8  4  8  8 12  4  0 12  4  8  8  8  0
 0  0 12  0  4  4  4  8  0  4  8  4  4  0 12  0  0 12 12 12  0  8  0  4  8  0 12  4  8  4  4  4  0  0 12  8  8 12 12  8  4 12 12  4  0  4 12  8  0  0  0 12  8 12  0  0  8  8 12  0  8 12  0  4  0  8  0  8  8  4 12  0  8  8  4  0
 0  0  0 12  4  0  4  4  8  0 12  4  4  4  8  0  8  8 12  0 12  4  8 12  4 12 12  4  0  0  4  0  8 12  0  8 12  4  4 12 12 12  8  4  8 12  8  0  8  4  4  0  0  0 12 12 12 12  0 12  0  8 12  0 12 12  0  8  4 12  4  8  0 12  0  0
 0  0  0  0  8  0  0  8  8  8  0  0  0  0  8  8  8  0  8  8  8  8  8  0  8  0  8  8  0  8  8  0  0  8  8  8  0  0  0  0  8  0  8  0  0  0  8  0  0  0  8  0  8  8  0  8  0  8  0  8  8  0  8  8  0  8  0  8  0  8  8  8  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  8  8  0  8  8  0  8  0  8  0  8  8  8  8  0  0  8  0  8  8  8  8  8  8  0  8  0  8  0  0  8  8  8  0  8  0  8  8  0  0  0  8  0  8  8  0  8  8  8  0  8  8  8  0  8  8  8  8  8  8  0  8  8  0  8  0

generates a code of length 76 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+34x^68+68x^69+103x^70+164x^71+99x^72+356x^73+293x^74+738x^75+530x^76+676x^77+286x^78+372x^79+56x^80+86x^81+60x^82+52x^83+34x^84+22x^85+17x^86+16x^87+11x^88+6x^89+6x^90+2x^91+2x^92+2x^93+2x^94+1x^96+1x^122

The gray image is a code over GF(2) with n=608, k=12 and d=272.
This code was found by Heurico 1.16 in 0.897 seconds.