The generator matrix

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

generates a code of length 72 over Z16 who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+376x^67+462x^68+916x^69+867x^70+1296x^71+771x^72+1080x^73+768x^74+784x^75+382x^76+304x^77+47x^78+56x^79+15x^80+16x^81+12x^82+16x^83+20x^85+1x^88+1x^94+1x^102

The gray image is a code over GF(2) with n=576, k=13 and d=268.
This code was found by Heurico 1.16 in 90 seconds.