The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+153x^68+164x^69+730x^70+840x^71+1675x^72+1564x^73+2388x^74+1520x^75+2372x^76+1564x^77+1570x^78+840x^79+633x^80+164x^81+108x^82+28x^84+24x^86+23x^88+12x^90+8x^92+3x^100

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 4.58 seconds.