The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  2  4  2  2  2  0  1  4  1  2  2  1  2  2  1  1  1
 0 12  0 12  0 12  0 12  0  4  8 12 12 12  0  0  8 12 12 12 12  4  4 12 12 12 12  0  0 12  0 12  0  0
 0  0  8  0  0  0  0  0  0  0  8  0  8  8  0  8  8  0  0  8  8  8  0  0  0  0  0  0  8  8  8  0  0  0
 0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  0  0  8  8  0  0  8  0  8  0  0  0  8  0  8  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  0  0  8  0  0  8  8  8  8  8  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  8  8  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  8  8  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  8  8  0  0  0  0  8  8  0  0  0
 0  0  0  0  0  0  0  8  0  8  0  8  0  8  0  8  8  0  8  0  8  8  8  8  0  0  8  8  8  0  8  8  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  8  8  0  8  0  8  8  0  8  8  8  0  8  0  0  8  8  0  0  0  0

generates a code of length 34 over Z16 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+61x^24+44x^26+214x^28+64x^29+184x^30+320x^31+888x^32+1664x^33+1328x^34+1664x^35+871x^36+320x^37+200x^38+64x^39+195x^40+36x^42+65x^44+7x^48+1x^52+1x^60

The gray image is a code over GF(2) with n=272, k=13 and d=96.
This code was found by Heurico 1.16 in 0.694 seconds.