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

generates a code of length 78 over Z16 who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+168x^74+426x^76+256x^77+508x^78+256x^79+199x^80+144x^82+77x^84+12x^86+1x^148

The gray image is a code over GF(2) with n=624, k=11 and d=296.
This code was found by Heurico 1.16 in 22.2 seconds.