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

generates a code of length 62 over Z16 who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+81x^52+134x^53+206x^54+420x^55+657x^56+1026x^57+1603x^58+2380x^59+3343x^60+4266x^61+4641x^62+4206x^63+3443x^64+2422x^65+1493x^66+1030x^67+567x^68+308x^69+209x^70+134x^71+81x^72+32x^73+30x^74+22x^75+17x^76+4x^77+7x^78+2x^80+1x^82+1x^86+1x^90

The gray image is a code over GF(2) with n=496, k=15 and d=208.
This code was found by Heurico 1.16 in 21.2 seconds.