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

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

Homogenous weight enumerator: w(x)=1x^0+46x^64+294x^65+539x^66+608x^67+1060x^68+1352x^69+1552x^70+2002x^71+1996x^72+1784x^73+1460x^74+1270x^75+923x^76+524x^77+369x^78+220x^79+188x^80+82x^81+33x^82+38x^83+7x^84+12x^85+13x^86+6x^87+2x^88+2x^90+1x^96

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 5.6 seconds.