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  1  1  1  1  1  1  1  2  2  1  2  2  2  1  1  1  4  1  2  4  2  4  1  2  2  1  8  2  1  2  1  1  2  1
 0 12  0  0  0  0  0  0  0  4 12 12  4  8  8 12  8  0 12 12  4  4  0 12  8  4 12  4 12  0 12  8  8  0 12  8  0  8  8  0 12  8  4 12  0  4  0  0 12  8 12 12  4 12  0  8  4 12  4  4  8 12  4  4  4  8  4 12
 0  0 12  0  0  0  4 12 12  4  4  0  8  0 12 12 12  8  8 12  4 12 12  0  0  4 12  8  0  4  8  0  8  0 12  8  0 12  0  8  8  4  4  0  4  8  4 12  0  8  4  8 12  8  8 12  8  4  4 12  8  4  4  4  8  8 12 12
 0  0  0 12  0  4  4  4  0  8  0  8 12  0  0 12 12  8  4 12 12  0  4  4 12  0  4  8  8  8  4  4  4  0 12  0  4 12  4  0  0  4  4 12 12  4  4  0  8  4  4  0  8 12 12  8  0  8 12 12  4  0  0 12  8  8  4 12
 0  0  0  0 12  4  8  4  4  0  4  4  0  0  8  4 12 12  4  4  8  4  0  8  4  0  8 12  8 12 12  0  0  0  8 12 12  0  4  0  4  4  4  8  0  0  8  8 12  8  0  4  0 12  0  4  8  4 12  4  4  4  8  0  4  4  4  8
 0  0  0  0  0  8  8  0  8  8  8  0  8  8  8  8  8  8  0  0  8  0  0  0  0  0  0  8  8  0  8  8  0  8  0  0  0  0  8  0  0  8  8  8  0  8  8  0  0  8  8  8  0  0  8  8  8  0  0  8  0  0  0  0  0  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+48x^59+110x^60+142x^61+166x^62+178x^63+246x^64+512x^65+694x^66+1196x^67+1714x^68+1202x^69+679x^70+460x^71+210x^72+190x^73+143x^74+64x^75+75x^76+56x^77+39x^78+34x^79+10x^80+10x^81+7x^82+4x^83+1x^84+1x^104

The gray image is a code over GF(2) with n=544, k=13 and d=236.
This code was found by Heurico 1.16 in 2.05 seconds.