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

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

Homogenous weight enumerator: w(x)=1x^0+131x^60+164x^61+439x^62+728x^63+891x^64+1276x^65+1654x^66+1932x^67+2058x^68+1988x^69+1657x^70+1324x^71+833x^72+500x^73+284x^74+228x^75+154x^76+40x^77+52x^78+12x^79+22x^80+9x^82+5x^84+1x^90+1x^96

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 5.67 seconds.