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

generates a code of length 68 over Z16 who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+309x^60+376x^61+1158x^62+980x^63+2034x^64+2096x^65+3842x^66+3172x^67+4852x^68+3476x^69+3980x^70+1896x^71+1927x^72+840x^73+842x^74+340x^75+345x^76+124x^77+118x^78+12x^79+30x^80+8x^82+5x^84+4x^86+1x^92

The gray image is a code over GF(2) with n=544, k=15 and d=240.
This code was found by Heurico 1.16 in 88.1 seconds.