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

generates a code of length 67 over Z16 who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+35x^58+84x^59+117x^60+186x^61+202x^62+302x^63+284x^64+800x^65+1450x^66+1410x^67+1462x^68+828x^69+246x^70+230x^71+105x^72+132x^73+78x^74+54x^75+64x^76+34x^77+27x^78+28x^79+14x^80+4x^81+9x^82+4x^83+1x^84+1x^102

The gray image is a code over GF(2) with n=536, k=13 and d=232.
This code was found by Heurico 1.16 in 2.04 seconds.