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

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

Homogenous weight enumerator: w(x)=1x^0+210x^61+473x^62+720x^63+932x^64+1414x^65+1601x^66+1848x^67+2182x^68+2148x^69+1478x^70+1242x^71+681x^72+554x^73+371x^74+192x^75+156x^76+86x^77+40x^78+26x^79+16x^80+4x^81+2x^82+4x^83+2x^86+1x^94

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 5.27 seconds.