The generator matrix

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

generates a code of length 68 over Z16 who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+105x^60+254x^61+568x^62+1084x^63+1867x^64+2664x^65+3689x^66+3848x^67+4600x^68+4174x^69+3601x^70+2658x^71+1784x^72+894x^73+447x^74+202x^75+160x^76+36x^77+37x^78+42x^79+24x^80+10x^81+8x^82+6x^83+2x^84+2x^86+1x^92

The gray image is a code over GF(2) with n=544, k=15 and d=240.
This code was found by Heurico 1.16 in 14.1 seconds.