The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  1  1  1  0  1  2  1  2  8  1  1  1  1  2 12  1  2  4  1  1  2  1  1  1  1  1  1  1  1  2  2  1  8  1  8  1  0  0  1  2  1  2  8  1  1
 0  2  0  6  4  6 12  2  6 14  8 12  0  2 10 12  0  6  4 14  6  2  8  2  2  2  0  6 10  2  2  2  8  0  0 14  2  2 10  2  8  4 10 10 12 14  8  2 14 10  8  6 14  2  2  8  2 12  2  2  6  4  4  6  2 14 14
 0  0 12  0  4  0  0  8  4 12  0  4  4  4  4  0  8  0  0  8 12  4 12  4 12  4  8  0  8  0  8  8  4 12 12  8  4  0  0  4  0  8  4  8  8  0  8  0  4  8  8 12  4  4 12  8  4  4  4  0  0  4  0  4  0  0  0
 0  0  0 12  0  0  0 12  4  8 12 12  4  0 12 12  8  0  4 12  4  8  8  8 12  4  4  8  0 12  4 12 12 12  8  4  4  4  8  0  4  0  4 12  4  0 12  8 12  4 12  4  0  4  8  8  0 12  4 12  4  4  0  4  4  4 12
 0  0  0  0  8  0  0  0  0  0  0  0  8  0  0  8  8  8  8  8  8  0  0  8  0  8  8  0  8  8  8  8  8  0  0  8  8  0  8  0  8  0  0  0  0  0  0  8  0  8  8  0  0  8  0  8  0  8  0  8  0  0  8  8  0  0  8
 0  0  0  0  0  8  0  8  0  8  8  8  8  0  8  8  0  0  8  0  0  0  8  8  8  0  0  0  8  0  0  8  0  0  8  8  8  0  0  0  0  8  8  8  0  0  0  8  8  8  8  0  0  0  0  0  8  0  0  8  8  0  0  8  8  0  8
 0  0  0  0  0  0  8  0  0  0  0  8  8  0  0  0  8  8  8  8  8  0  8  0  8  0  0  8  8  8  0  0  0  0  0  8  8  8  8  8  8  8  8  8  0  8  8  0  0  8  0  8  0  8  8  0  8  8  0  8  8  0  8  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+61x^58+108x^59+244x^60+356x^61+452x^62+846x^63+1244x^64+1682x^65+2098x^66+2252x^67+2217x^68+1696x^69+1153x^70+826x^71+434x^72+270x^73+157x^74+102x^75+62x^76+26x^77+31x^78+24x^79+17x^80+12x^82+2x^83+5x^84+2x^85+3x^86+1x^94

The gray image is a code over GF(2) with n=536, k=14 and d=232.
This code was found by Heurico 1.16 in 6.35 seconds.