The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  8  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  0  2 12  2  2
 0  2  0  2  8  0 10  2  4  6  4 14  4 14 12 14  0  8 10 14 10  0  4  2 10 12  6  0  4 14  4 14 10  8  2  2 12  6 12  4  6  2  6  4 10  4  8  2  6  0 14 10  8  8 12 10  6 12 10 12  6  6 10  4  6  6 14  2  4  0  2  2
 0  0  2  2  4  6  6  4  4 14  2 12  6 10  0  8  0  2 14  4  2 12 10  4  8  4 10 14 14 14  8  8  0  2 12  6  8  8 10  0  8 10  2  4  4 10 10  2 12  4 10  0  6  0  6  8  4 12 12  4  2  6  6  8  6  0  2 12  2  2 10 10
 0  0  0  8  8  8  0  8  0  8  8  0  0  0  8  8  8  8  8  8  0  0  0  0  8  8  8  0  8  0  0  0  0  0  0  0  0  8  0  8  0  8  0  8  0  8  8  0  0  8  8  0  0  8  8  0  8  8  0  0  8  0  8  8  8  0  0  0  0  8  0  8

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

Homogenous weight enumerator: w(x)=1x^0+196x^68+84x^69+212x^70+312x^71+522x^72+288x^73+192x^74+72x^75+98x^76+12x^77+12x^78+44x^80+2x^84+1x^128

The gray image is a code over GF(2) with n=576, k=11 and d=272.
This code was found by Heurico 1.16 in 0.781 seconds.