The generator matrix

 1  0  1  1  1  6  1 12  1  1  1 10  1  1  8  1 14  1  1  1  4  1  1  2  1  1  0  1  6  1  1  1  0  6  1  1  1  1  4  2  1  1  1  4  1  1  2  1  2  4  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  1  1  1  1  1  1  1 12  1  1  1 12  1 14  1  1 12
 0  1 11  6  5  1  9  1 12  3 10  1 15  8  1 14  1 13  7  4  1  2  1  1  0  3  1  6  1 15 13  0  1  1  2 11  1  6  1  1  4  7  4  1  9  2  1  5  6  2  5 11 15  5 15 11  9  9 13  3 15  8  5  9  5 15 11  6  6  0  0 10 10  2  0  5 12  1 10  1  5  4  2
 0  0 12  0  0  8  0  8  8  8  8  0  8  4  4 12 12  4  4  4  4 12 12 12  0  8  0  0  0  8  4  4  4  4  4 12 12 12 12 12 12  4  0  0  8  0  0  8  8 12 12  8  0  8 12  4 12  4  0  4 12  4  8 12  0  0  8  0  8 12  4  8  0 12  8  4  8  8  0 12  0  4  8
 0  0  0  8  0  8  8  0  8  8  0  8  0  0  8  8  0  0  8  8  8  0  8  0  0  8  8  8  0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  8  0  0  0  8  8  8  8  0  0  0  8  8  0  0  0  0  0  8  8  0  8  8  0  0  0  8  8  8  8  8  8  0  0  0  8  0  8  0  8
 0  0  0  0  8  8  8  8  8  0  8  0  0  0  8  0  8  8  0  8  0  8  8  0  8  8  8  8  8  8  0  8  0  8  0  8  0  8  8  0  0  8  0  0  0  0  0  0  0  8  8  8  8  0  0  0  0  0  0  8  8  8  8  8  8  0  0  8  8  8  8  8  8  8  0  8  0  0  0  0  0  0  8

generates a code of length 83 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+158x^78+236x^79+540x^80+524x^81+491x^82+372x^83+544x^84+416x^85+363x^86+180x^87+146x^88+44x^89+33x^90+12x^91+6x^92+8x^93+3x^94+7x^96+8x^98+2x^100+1x^104+1x^120

The gray image is a code over GF(2) with n=664, k=12 and d=312.
This code was found by Heurico 1.16 in 0.806 seconds.