The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  2  2  1  2  1  1  4  2  1  4  1  4  2  1  1  4  4  1  2  1  1  1  1  2  1  2  2  1  2  1  1  2  2  0  2  8  1 12  2  2 12  8  0  1
 0  2  0  0  0  2  6 14  8  8 14  6 12  2  8 10  2  6 12  0  2  0 12 14  2  4 12 14  8 10  2  4 10 10 14  4 14  2  2 12  8  4 10  2  6 10  8  2  2  0 12  2 12  8 14 14  0 12  2  2  4  2  6  0  0  8  6  2  0  2 10 12  2  4 12  0
 0  0  2  0  2  2 10  0 12 14  8  2 12  4  2  2  8 12 10 14 10  4 12  2 14  6  8  6  8  6  4  2 12 12  2 10 14 12 10  8 10 12  8  4  4 10  4 12 14 14 12  4  8  0 14  8  6  6  6 12 10  6  0  0  8  8 14  6  0  0  8  8  2  2  2  0
 0  0  0  2  2  8 10  2  4  0 14 12  2 12  6 14 14 12 10 12 12 10  0 14  2  8  0  8  2 12 14  4 12 10  6 10  2  0  0  2 12  2 12 10  2  4  8  8 14  2 14  6 14  0 14 12  2 10 14 10  4  0  8  2  2  2  0 14  4  0  8  6  2 10  8  8
 0  0  0  0  8  8  0  8  8  8  0  0  8  8  0  8  8  8  8  8  8  0  8  8  0  0  0  0  8  8  0  8  0  8  0  8  8  0  8  8  8  8  8  8  0  0  0  8  0  8  8  8  8  8  8  0  0  8  0  8  0  0  8  0  8  0  8  8  8  0  8  0  8  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+60x^68+296x^69+470x^70+812x^71+1114x^72+1334x^73+1553x^74+1732x^75+2047x^76+1768x^77+1460x^78+1218x^79+875x^80+586x^81+330x^82+314x^83+197x^84+84x^85+54x^86+34x^87+20x^88+12x^89+2x^90+2x^91+6x^92+2x^94+1x^98

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 6.09 seconds.