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  1  1  1  8  1  2  1  1  1  2  1  1  8  1  1  4  1  1  2  2  1  0  2  1  1  1  1  1  2  1  4 12  1  1
 0  2  0  6  4  6 12  2  0  6  8 14  4  2  4 10  8  2  6  4  4 10 12  2  8  6  8 14  8 10  8 10  8 10 14 12 14 12 12 14  0  2  8  8  6 12  6  2 10  2 12  2 12  6 10  0  8 14  4 14  2  2  2  4 12 14 10  8  2  2 10  4  8  4  2 12  6  2  2  2 14 14
 0  0 12  0  4  0  8  0  4  4  0  4  4 12  0 12  8  4  8 12  0  8 12  4  0  8  4  4  8 12 12  8  8 12  0  0  8 12  0 12 12  0  4  4  8  0 12  0  4  8  4 12  4 12 12  0  8  4 12  8  0 12  8 12  4  4 12  4  8  8  0  4  0  4  0  0  0  4 12 12  8  0
 0  0  0 12  0  8  8  4  4  4  4  0 12  0  4  4 12  0  8  8  0  4  4  4  8 12  8  8 12 12  4  8  4  4  0  8  8 12  4 12  8 12  4  0 12  0  0  8  0  0  4  8  8  4  8  4  0  8 12  4 12  8 12  0  8  0  4  8 12  0  4  0  0 12  8 12  8  8  8 12  0 12
 0  0  0  0  8  8  8  8  0  0  0  8  8  0  8  8  0  0  8  8  8  8  8  8  0  0  0  8  8  0  0  0  8  0  8  8  0  0  0  8  8  0  8  0  8  0  0  0  8  8  0  8  8  0  0  8  8  0  8  8  8  8  8  0  0  0  8  8  0  8  8  0  8  0  8  0  8  0  0  0  0  8

generates a code of length 82 over Z16 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+168x^76+60x^77+296x^78+248x^79+514x^80+468x^81+718x^82+480x^83+472x^84+212x^85+172x^86+40x^87+120x^88+28x^89+54x^90+35x^92+8x^94+1x^96+1x^140

The gray image is a code over GF(2) with n=656, k=12 and d=304.
This code was found by Heurico 1.16 in 1.35 seconds.