The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+65x^60+338x^61+513x^62+1420x^63+1746x^64+2700x^65+3208x^66+4296x^67+4398x^68+4302x^69+3283x^70+2828x^71+1465x^72+1040x^73+502x^74+318x^75+122x^76+120x^77+39x^78+28x^79+4x^80+8x^81+6x^82+6x^83+7x^84+4x^85+1x^86

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 14.2 seconds.