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

generates a code of length 72 over Z16 who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+210x^67+296x^68+392x^69+443x^70+536x^71+535x^72+550x^73+382x^74+274x^75+146x^76+112x^77+93x^78+64x^79+22x^80+18x^81+20x^83+1x^90+1x^114

The gray image is a code over GF(2) with n=576, k=12 and d=268.
This code was found by Heurico 1.16 in 18.1 seconds.