The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+226x^68+1502x^69+2828x^70+4596x^71+5441x^72+6580x^73+7585x^74+8274x^75+7996x^76+6822x^77+5196x^78+3920x^79+2169x^80+1312x^81+509x^82+342x^83+134x^84+52x^85+30x^86+4x^87+9x^88+4x^89+4x^90

The gray image is a code over GF(2) with n=600, k=16 and d=272.
This code was found by Heurico 1.16 in 41.1 seconds.