The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 14  2  1  1  1  0  1  8  1  1  1  6  1 14  1  1  1  1  1  4  1  0  1  1  6  1  1 10 14  1  1  1  8  1 10  1 10  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  8  1  4  8
 0  1 11  6 13  1  0  7  1 14  5  1  1  6  3  4  1  9  1  2  5  0  1 15  1  1  6 15  4  2  1 11  1 10  5  1 13 12  1  1  4  0  6  1 11  1 12  1  1  6 11  8  3  2  1 13  0  6  6  5  1 14  5 14  2 11  4  1
 0  0 12  0  4  0  0  4  0  4  0  4 12  0  8  8  4  8  8  0  4  4 12  8  0  0 12  4  4  4  8  8 12  0 12 12 12  8  0  0  8  0  4  8  0 12  4 12  4 12  0  8  4 12  4  4  0  8  0  8  0 12  0  0 12  8  4  8
 0  0  0 12  0  0 12  8  0  8  8  0  0  8  8  4  4  0 12 12 12  4  4  0  4  4  4  4  8  8 12  4  4  0  4  4  8  0  8 12  4  0 12 12  4  8  4 12  4  4 12  8 12  8  0  8  0 12  0  4  8  4  4 12 12  4  0 12
 0  0  0  0  8  0  0  8  8  8  0  8  0  8  0  8  0  8  0  8  0  8  8  8  8  0  8  8  8  0  0  0  0  8  0  8  0  8  0  0  8  0  8  8  8  0  0  0  8  0  0  0  8  0  8  0  8  8  8  0  8  0  8  8  0  0  0  8
 0  0  0  0  0  8  0  8  0  0  8  8  8  0  0  0  0  8  8  8  0  8  8  0  8  0  0  0  8  0  0  8  8  8  0  0  0  0  8  8  0  8  8  0  8  8  0  0  8  0  0  0  8  8  0  8  8  8  0  0  8  8  8  8  8  8  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  8  8  8  8  0  0  8  8  8  8  0  8  8  8  8  8  0  0  8  8  0  8  0  8  8  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+50x^59+169x^60+302x^61+559x^62+902x^63+1940x^64+2078x^65+4383x^66+3384x^67+5578x^68+3342x^69+4078x^70+2018x^71+2015x^72+872x^73+540x^74+268x^75+121x^76+42x^77+26x^78+24x^79+27x^80+18x^81+13x^82+10x^83+4x^84+2x^85+1x^88+1x^94

The gray image is a code over GF(2) with n=544, k=15 and d=236.
This code was found by Heurico 1.16 in 15.2 seconds.