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

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

Homogenous weight enumerator: w(x)=1x^0+42x^59+64x^60+148x^61+188x^62+208x^63+215x^64+750x^65+411x^66+1950x^67+377x^68+1964x^69+389x^70+746x^71+163x^72+138x^73+107x^74+84x^75+56x^76+62x^77+51x^78+38x^79+17x^80+8x^81+6x^82+4x^83+2x^84+2x^85+1x^108

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 2.09 seconds.