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

generates a code of length 63 over Z16 who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+298x^56+284x^57+780x^58+776x^59+1491x^60+1524x^61+2098x^62+2108x^63+2209x^64+1424x^65+1274x^66+720x^67+673x^68+276x^69+234x^70+44x^71+112x^72+12x^73+26x^74+11x^76+4x^78+4x^80+1x^84

The gray image is a code over GF(2) with n=504, k=14 and d=224.
This code was found by Heurico 1.16 in 89.9 seconds.