The generator matrix

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

generates a code of length 71 over Z16 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+537x^68+608x^70+404x^72+344x^74+140x^76+8x^78+3x^80+2x^84+1x^116

The gray image is a code over GF(2) with n=568, k=11 and d=272.
This code was found by Heurico 1.16 in 60.8 seconds.