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

generates a code of length 68 over Z16 who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+88x^61+218x^62+324x^63+429x^64+612x^65+838x^66+1094x^67+1147x^68+1032x^69+880x^70+574x^71+390x^72+218x^73+126x^74+94x^75+34x^76+30x^77+12x^78+14x^79+12x^80+2x^81+4x^82+12x^83+2x^84+2x^85+2x^86+1x^100

The gray image is a code over GF(2) with n=544, k=13 and d=244.
This code was found by Heurico 1.16 in 15.3 seconds.