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

generates a code of length 68 over Z16 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+347x^62+24x^63+882x^64+224x^65+1258x^66+752x^67+1494x^68+832x^69+1033x^70+184x^71+647x^72+32x^73+288x^74+106x^76+73x^78+5x^80+6x^82+3x^86+1x^104

The gray image is a code over GF(2) with n=544, k=13 and d=248.
This code was found by Heurico 1.16 in 45.7 seconds.