The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+308x^76+424x^78+272x^80+8x^82+8x^84+1x^88+1x^104+1x^112

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 0.636 seconds.