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

generates a code of length 68 over Z16 who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+204x^59+596x^60+1026x^61+1512x^62+2428x^63+3497x^64+4702x^65+6776x^66+7948x^67+8198x^68+8266x^69+6760x^70+4768x^71+3282x^72+2206x^73+1430x^74+826x^75+510x^76+286x^77+183x^78+80x^79+12x^80+24x^81+10x^82+2x^83+2x^85+1x^94

The gray image is a code over GF(2) with n=544, k=16 and d=236.
This code was found by Heurico 1.16 in 72.4 seconds.