The generator matrix

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

generates a code of length 84 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+44x^78+134x^79+381x^80+442x^81+396x^82+384x^83+631x^84+468x^85+327x^86+302x^87+292x^88+170x^89+55x^90+12x^91+32x^92+8x^93+7x^94+6x^96+1x^98+2x^110+1x^132

The gray image is a code over GF(2) with n=672, k=12 and d=312.
This code was found by Heurico 1.16 in 0.615 seconds.