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

generates a code of length 71 over Z16 who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+339x^66+76x^67+559x^68+240x^69+730x^70+400x^71+676x^72+232x^73+420x^74+68x^75+196x^76+8x^77+94x^78+34x^80+17x^82+5x^84+1x^112

The gray image is a code over GF(2) with n=568, k=12 and d=264.
This code was found by Heurico 1.16 in 1.47 seconds.