The generator matrix

 1  0  1  1  1  6  1  1 12  1 10  1  1  8  1  1 14  1  1  1  2  1  1  0  1  1  4  1  1  2  8  1  1  1  1  6  1 10 14  1  1  1  2  0 10  6  4  1  4  1  1  1 12  1  1  1  1  1  6  1  1  1  1  1  1  0 12  0  0  1  2  0  8  2  1
 0  1 11  6 13  1  8  7  1  1  1 10  3  1 12  5  1 14  4  9  1  6 11  1  2  8  1  9  3  1  1  5 10 15  4  1 14  1  1  5  4  7  1  1  1  1  1  6  1  0  4 15  1 12 13 10  6  4  1  0  4 10  5 10 14  1  1  1  1  5  8  2  2  0  0
 0  0 12  0  4  0  4  4  8  4  0  0  8  4  8  8  4  4 12  8  4  0 12  0 12 12 12  0  8  4  4  8  0  8  4  0  4  0  4  0 12 12  0  0  8 12  4  0 12  8  0  8  0 12  4  0  4 12  8  0  8 12 12  4 12 12  4 12  4  8  4  4  4 12  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  8  8  0  0  8  8  0  8  0  8  0  0  8  0  8  8  0  8  0  0  8  0  8  8  0  8  8  8  0  0  8  0  8  8  8  8  8  0  0  0  0  0  8  0  8  0  8  8  0
 0  0  0  0  8  0  0  0  8  8  8  0  0  0  8  8  8  8  0  0  0  8  8  8  0  8  8  0  0  8  0  8  8  0  0  0  8  0  8  8  0  8  8  0  0  8  0  8  8  8  8  0  0  8  0  0  0  8  8  0  8  0  8  0  0  8  8  0  8  0  0  0  8  0  8
 0  0  0  0  0  8  0  8  0  8  8  8  8  8  8  8  8  0  8  0  0  8  0  0  0  8  0  8  0  8  8  0  0  0  8  0  8  0  0  8  0  8  0  8  8  0  0  8  8  0  0  8  0  0  0  0  8  8  8  8  8  8  0  8  0  0  8  0  8  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+32x^68+164x^69+255x^70+612x^71+588x^72+1004x^73+942x^74+1192x^75+938x^76+876x^77+538x^78+520x^79+220x^80+186x^81+48x^82+40x^83+6x^84+6x^85+5x^86+4x^87+6x^88+2x^89+1x^90+2x^93+2x^94+1x^96+1x^106

The gray image is a code over GF(2) with n=600, k=13 and d=272.
This code was found by Heurico 1.16 in 1.34 seconds.