The generator matrix

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

generates a code of length 75 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+81x^68+350x^69+676x^70+1098x^71+1487x^72+1780x^73+1872x^74+1944x^75+2108x^76+1698x^77+1178x^78+896x^79+544x^80+276x^81+166x^82+86x^83+46x^84+46x^85+20x^86+4x^87+4x^88+8x^89+6x^90+2x^91+1x^92+2x^93+2x^94+2x^95

The gray image is a code over GF(2) with n=600, k=14 and d=272.
This code was found by Heurico 1.16 in 4.41 seconds.