The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+50x^68+122x^69+275x^70+594x^71+1140x^72+1226x^73+1859x^74+1942x^75+2137x^76+1936x^77+1806x^78+1190x^79+1112x^80+510x^81+248x^82+98x^83+28x^84+32x^85+21x^86+8x^87+7x^88+8x^89+8x^90+8x^91+4x^92+6x^93+5x^94+1x^98+1x^100+1x^102

The gray image is a code over GF(2) with n=608, k=14 and d=272.
This code was found by Heurico 1.16 in 4.68 seconds.