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

generates a code of length 69 over Z16 who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+62x^61+139x^62+182x^63+259x^64+340x^65+879x^66+474x^67+1536x^68+506x^69+1556x^70+452x^71+890x^72+292x^73+270x^74+148x^75+54x^76+70x^77+23x^78+22x^79+8x^80+8x^81+11x^82+2x^83+2x^84+2x^85+2x^86+1x^88+1x^104

The gray image is a code over GF(2) with n=552, k=13 and d=244.
This code was found by Heurico 1.16 in 1.86 seconds.