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

generates a code of length 34 over Z16 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+566x^32+32x^34+336x^36+32x^38+56x^40+1x^64

The gray image is a code over GF(2) with n=272, k=10 and d=128.
This code was found by Heurico 1.16 in 0.0401 seconds.