The generator matrix

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

generates a code of length 68 over Z16 who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+127x^58+44x^59+462x^60+392x^61+1377x^62+1708x^63+3313x^64+4704x^65+7309x^66+8468x^67+9641x^68+8576x^69+7581x^70+4740x^71+3233x^72+1632x^73+1076x^74+400x^75+394x^76+56x^77+158x^78+89x^80+36x^82+18x^84+1x^92

The gray image is a code over GF(2) with n=544, k=16 and d=232.
This code was found by Heurico 1.16 in 57.2 seconds.