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

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

Homogenous weight enumerator: w(x)=1x^0+58x^60+280x^61+389x^62+600x^63+1060x^64+1160x^65+1812x^66+1562x^67+2649x^68+1696x^69+1913x^70+1024x^71+827x^72+508x^73+345x^74+228x^75+95x^76+86x^77+45x^78+8x^79+10x^80+10x^81+7x^82+2x^83+2x^84+2x^85+2x^88+2x^89+1x^94

The gray image is a code over GF(2) with n=544, k=14 and d=240.
This code was found by Heurico 1.16 in 5.68 seconds.