The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+412x^68+432x^69+676x^70+360x^71+548x^72+360x^73+504x^74+312x^75+314x^76+72x^77+52x^78+34x^80+16x^82+1x^84+1x^96+1x^100

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 1.24 seconds.