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

generates a code of length 78 over Z16 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+198x^76+128x^77+384x^78+128x^79+175x^80+9x^84+1x^148

The gray image is a code over GF(2) with n=624, k=10 and d=304.
This code was found by Heurico 1.16 in 4.09 seconds.