The generator matrix

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

generates a code of length 72 over Z16 who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+56x^65+123x^66+368x^67+446x^68+764x^69+630x^70+1104x^71+1203x^72+1132x^73+663x^74+784x^75+374x^76+340x^77+112x^78+48x^79+19x^80+12x^81+3x^82+2x^84+2x^86+1x^88+1x^90+2x^92+2x^98

The gray image is a code over GF(2) with n=576, k=13 and d=260.
This code was found by Heurico 1.16 in 15.7 seconds.