The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+37x^64+132x^65+289x^66+500x^67+878x^68+1444x^69+1905x^70+2044x^71+2059x^72+2062x^73+1872x^74+1390x^75+818x^76+488x^77+249x^78+86x^79+27x^80+24x^81+28x^82+6x^83+16x^84+4x^85+5x^86+6x^87+3x^88+6x^89+2x^90+1x^94+1x^96+1x^98

The gray image is a code over GF(2) with n=576, k=14 and d=256.
This code was found by Heurico 1.16 in 4.31 seconds.