The generator matrix

 1  0  1  1  6  1  1  1  4  1  1  8  2  1  1  1 14  1  1  6  1  1  8  1  1  1  2  1  1  1  0  1  1 10  1  1 12  1  1  1  0  1  1  0 10  4  8  8 14 12  6  1  1  1  1  8  6  1  4  1  0 14  1  1  1  6  1  0
 0  1  1  6  1  3  5  4  1  7  2  1  1  9  8  3  1 14 15  1  6  7  1 12  9 12  1  5 12 11  1  6 12  1 11 13  1 13  2  0  1  1  2  1  1  4  2  1  1 12  1 13  7 12 12  1  1  3  8 10  1  1  7  1 14  1  7  1
 0  0  2  0  0  0  0  2  2  2 10 12  2  8  4 14  4  4  8  6 14  4  2 14  6 10  4  6  8  4 14  0  0  6  2  4  6 10  4 14 12 12  4  8  8  2 14  8  4  2 14  2  6  4 12  2  2  8  2  0 12 10 10  0 12 14 12  0
 0  0  0  8  0  0  0  0  0  0  0  0  8  8  0  8  0  0  0  8  8  8  0  0  8  0  8  8  0  8  8  0  8  8  0  8  0  8  0  8  0  0  8  8  0  8  0  8  8  8  8  0  0  8  0  8  8  0  0  8  8  8  8  0  8  0  8  0
 0  0  0  0  8  0  0  8  8  8  0  0  0  0  8  8  0  0  8  0  0  8  8  8  8  0  8  8  0  8  0  8  8  8  8  0  0  0  8  0  8  8  0  8  8  8  0  8  0  8  8  0  0  8  8  8  8  8  8  8  8  8  0  0  0  0  0  8
 0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  8  8  8  8  8  8  8  0  8  0  8  0  0  0  8  0  0  8  8  0  0  8  8  8  0  0  8  0  8  0  8  8  0  0
 0  0  0  0  0  0  8  0  8  8  8  8  0  8  8  8  0  8  8  8  0  8  0  0  8  8  0  0  0  0  8  8  0  0  0  8  0  8  0  8  8  0  0  0  0  8  0  8  0  0  8  0  8  0  0  0  8  8  8  8  8  0  0  0  8  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+80x^60+240x^61+608x^62+1018x^63+1839x^64+3006x^65+3269x^66+4280x^67+4049x^68+4946x^69+3078x^70+2720x^71+1645x^72+842x^73+532x^74+278x^75+179x^76+46x^77+53x^78+20x^79+15x^80+8x^81+10x^82+2x^83+1x^86+2x^87+1x^90

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 14 seconds.