The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+114x^58+28x^59+430x^60+300x^61+1190x^62+1628x^63+3460x^64+4548x^65+7270x^66+8812x^67+10034x^68+8828x^69+7326x^70+4772x^71+3344x^72+1452x^73+1018x^74+312x^75+335x^76+40x^77+164x^78+81x^80+34x^82+9x^84+4x^86+1x^88+1x^96

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 57.3 seconds.