The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+207x^60+168x^61+542x^62+1064x^63+1820x^64+2636x^65+3522x^66+4332x^67+4321x^68+4312x^69+3618x^70+2752x^71+1613x^72+860x^73+424x^74+236x^75+180x^76+24x^77+62x^78+37x^80+22x^82+11x^84+2x^86+1x^88+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 50.9 seconds.