The generator matrix

 1  0  1  1  1  6  1  1 12  1 10  1  1  1  0  1  1  6 12  1  1  1  1 10  1  1  0  1  1 10  1  1  6  1  1 12  1  0  1  1  1  6  1  1  8  1  1 14  1  2  2  1  2  1  1  1  1  2  2  1  1  1  0  1 12  2 12 10 12  0  2
 0  1  3  6  5  1 12 15  1 10  1  9  3  0  1  6  5  1  1 12 15 10  9  1  0  3  1  6  5  1 10  9  1 12 15  1  0  1  3  6  5  1  8 11  1 14 13  1 12  0 12 10  8  0 12 10  6  6 14 15  0  8  2  7  2  6  1  1  2  4  6
 0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  8  0  0  0  0  8  8  8  0  0  0  0  8  8  0  8  0  8  0  8  8  8  8  0  8  0  8  0  0  8  8  0  8  8  8  0  0  0  8  0  0  0  8  0  0  8  0  8
 0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  0  8  0  8  0  0  8  8  0  8  8  0  0  0  8  8  8  0  8  0  0  8  8  8  0  0  8  0  8  0  0  0  8  0  8  8  0  8  0  0  0  8  0  8  0  0  0  8  8  0  0  8  0  8  0  8
 0  0  0  0  8  0  0  8  0  0  0  8  8  8  8  8  0  8  8  8  0  8  0  8  0  8  0  0  0  8  8  8  0  0  8  8  8  0  0  0  0  0  8  0  8  8  8  8  8  0  8  8  0  0  0  8  0  0  8  0  0  0  8  0  8  0  8  8  0  0  0
 0  0  0  0  0  8  8  8  8  8  0  0  8  8  8  0  8  0  0  8  8  0  0  8  0  0  8  0  8  0  8  8  0  8  0  8  0  0  0  8  0  8  0  8  0  8  8  8  8  0  0  0  8  8  0  0  8  0  8  0  8  0  0  0  8  8  0  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+261x^66+168x^67+569x^68+232x^69+767x^70+240x^71+701x^72+240x^73+510x^74+104x^75+169x^76+40x^77+61x^78+30x^80+2x^84+1x^122

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 18.3 seconds.