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

generates a code of length 81 over Z16 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+308x^76+152x^77+576x^78+280x^79+659x^80+208x^81+644x^82+208x^83+633x^84+152x^85+184x^86+24x^87+57x^88+4x^90+2x^92+1x^100+3x^104

The gray image is a code over GF(2) with n=648, k=12 and d=304.
This code was found by Heurico 1.16 in 3.99 seconds.