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

generates a code of length 72 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+18x^68+32x^69+72x^70+96x^71+586x^72+96x^73+72x^74+32x^75+17x^76+1x^80+1x^140

The gray image is a code over GF(2) with n=576, k=10 and d=272.
This code was found by Heurico 1.16 in 0.313 seconds.