The generator matrix

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

generates a code of length 72 over Z16 who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+98x^64+584x^65+1350x^66+2578x^67+3495x^68+5816x^69+6846x^70+7934x^71+8180x^72+8596x^73+6602x^74+5496x^75+3488x^76+2248x^77+1099x^78+632x^79+241x^80+124x^81+66x^82+28x^83+14x^84+8x^85+5x^86+2x^88+2x^91+1x^92+2x^95

The gray image is a code over GF(2) with n=576, k=16 and d=256.
This code was found by Heurico 1.16 in 43.9 seconds.