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  1  1  1  2  1  1  1  1  1  8  2  1  4  1 12  1  1 12  1  1  1  2  2  1 12  1 12  1  0  1  1  1  2  2  2  0  0  1  4 12  1  2  8  1
 0  2  0  0  8 10  6  6  8 10  0 14  0 10  2 12  4  2  4 12  6 14  0  2  4 14  2  0 12  2 12 14  8  6  4  0  2 12  2 12 10  8  6  2 10  8  8 14  4  6  6 14  4  4  4 12  2  2  8  8  2  2 14  0  2  4 10  8  8 12 12  8  4
 0  0  2  0 10 10 10  8  0 10  8  2 14  0 12 10 12 12  4 14 14 12 10  2 14  0  6 12  4  4 14 12  2 10  8 10 14 12 10 10  2  4  6 14 12 14  2  2  2 14  0 14  8  2  6  0  0 14 12 14  6  0  6 10 12 12 14  2  2  4  2  2 10
 0  0  0  2  2  8 10  2  4  4  6  6 14  6 12  4  4  2 10 10  8 12 12  6  4  4 14  2  8  6  6  0  6 12  0  6  4 14  6  0 10  2  2 12  0  8  0  8  2 14 12 14  8 12  0  2 10  2  4  2  0  0 10  4 14  2 14  6 12 12 14  2  8

generates a code of length 73 over Z16 who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+270x^67+262x^68+706x^69+566x^70+1008x^71+1072x^72+992x^73+918x^74+750x^75+460x^76+434x^77+193x^78+256x^79+83x^80+132x^81+17x^82+48x^83+10x^84+8x^85+1x^86+4x^87+1x^106

The gray image is a code over GF(2) with n=584, k=13 and d=268.
This code was found by Heurico 1.16 in 5.28 seconds.