The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+41x^58+108x^59+439x^60+720x^61+1356x^62+2286x^63+3529x^64+4784x^65+7076x^66+8080x^67+8970x^68+7902x^69+7067x^70+4932x^71+3562x^72+2024x^73+1239x^74+670x^75+361x^76+168x^77+104x^78+44x^79+28x^80+16x^81+4x^82+6x^83+6x^84+2x^85+9x^86+2x^87

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 52 seconds.