The generator matrix

 1  0  1  1  1 14  1  1  0 14  1  1  1  0  1  2  1  1  1  8  1  1  1  2  1  1 10  1  1 14  1  1  8  1  1  1  0  1 10  1 14  4  1  1  1  1  1  1 10  1 12  1  1  6 10  1  1  1  1  1 12 12  2  1  1  1 14  6
 0  1 11  6  1  1  8  3  1  1 14  9  6  1  3  1 13  0  3  1  5  2  0  1 15  2  1  4 11  1  8 11  1  2  1 12  1 13  1  9  1  1  0 14  9 10 15  6  1  1  1  4 15  1  1  3 15  4 14 10  2  1  1 12  7 15  1  1
 0  0 12  0  0  0  0  8 12  4  4  4 12 12  0  4  8  8 12  8  4 12 12  0  0  8  8  4  0 12  8  4  8  0 12  4  8  8  4 12  4 12  4  0  4  0  0 12  8  0  8  4  0  0  8  4  0 12  0 12 12  8 12  0  0  8  4  4
 0  0  0 12  0  0  8  8  8  8  0  8  8 12 12 12 12 12 12 12 12 12  4  4  4  4  4 12  4  8  0 12  4  8  8  0  8  0  8 12  0  4  0  0  4  4  0 12  0  8  4  4 12  4  0  4  0 12  8  0 12  4  0  8 12  0  8  4
 0  0  0  0  4 12 12  8  4  0  0  4  4  8 12  4  0  4 12  4  8  4  8  8  4  8  4 12  0  4 12  8  8  8  8  0 12  4 12  0  8 12  8  0  4  4  8  8  4  0 12  0  4  0  0 12  4  4  4 12 12  4 12  0  8  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+84x^61+268x^62+440x^63+999x^64+1474x^65+1834x^66+2134x^67+2097x^68+2116x^69+1834x^70+1436x^71+846x^72+400x^73+224x^74+66x^75+31x^76+18x^77+26x^78+16x^79+21x^80+2x^81+4x^82+4x^83+4x^84+2x^85+1x^88+2x^90

The gray image is a code over GF(2) with n=544, k=14 and d=244.
This code was found by Heurico 1.16 in 4.07 seconds.