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

generates a code of length 72 over Z16 who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+24x^69+132x^70+108x^71+527x^72+32x^73+171x^74+28x^75+1x^130

The gray image is a code over GF(2) with n=576, k=10 and d=276.
This code was found by Heurico 1.16 in 0.202 seconds.