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

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

Homogenous weight enumerator: w(x)=1x^0+46x^59+155x^60+228x^61+290x^62+506x^63+860x^64+1278x^65+1826x^66+2098x^67+1964x^68+2046x^69+1817x^70+1246x^71+886x^72+470x^73+240x^74+164x^75+79x^76+50x^77+40x^78+32x^79+18x^80+20x^81+6x^82+4x^83+2x^84+4x^85+5x^86+2x^88+1x^96

The gray image is a code over GF(2) with n=544, k=14 and d=236.
This code was found by Heurico 1.16 in 6.53 seconds.