The generator matrix

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

generates a code of length 72 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+96x^68+684x^69+662x^70+828x^71+354x^72+444x^73+216x^74+272x^75+182x^76+152x^77+60x^78+92x^79+21x^80+24x^81+6x^82+2x^88

The gray image is a code over GF(2) with n=576, k=12 and d=272.
This code was found by Heurico 1.16 in 0.275 seconds.