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

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

Homogenous weight enumerator: w(x)=1x^0+115x^72+8x^76+3x^80+1x^88

The gray image is a code over GF(2) with n=576, k=7 and d=288.
This code was found by Heurico 1.16 in 0.252 seconds.