The generator matrix

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

generates a code of length 76 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+51x^68+344x^69+746x^70+1414x^71+1992x^72+2504x^73+3429x^74+3880x^75+4032x^76+4204x^77+3668x^78+2506x^79+1589x^80+1050x^81+613x^82+318x^83+176x^84+88x^85+51x^86+56x^87+22x^88+18x^89+3x^90+2x^91+7x^92+1x^94+2x^96+1x^98

The gray image is a code over GF(2) with n=608, k=15 and d=272.
This code was found by Heurico 1.16 in 15.5 seconds.