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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+203x^54+452x^55+899x^56+1284x^57+1753x^58+2744x^59+2919x^60+4276x^61+3892x^62+4256x^63+3015x^64+2716x^65+1580x^66+1160x^67+776x^68+412x^69+213x^70+92x^71+61x^72+16x^73+35x^74+9x^76+4x^78

The gray image is a code over GF(2) with n=496, k=15 and d=216.
This code was found by Heurico 1.16 in 17.4 seconds.