The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  2  1  1  4  2  1  1  1  1  1  2  2  2  4  4  4  2  1  1
 0 12  0  4  0  0  4 12  0  8  4  4  8 12  4 12  8  4  4  8  8  4  4  4  0 12  4 12 12  0 12 12  0  0
 0  0 12  4  0 12  4  0  0  4  0 12  4  0  4  8 12  4  4  4 12 12  8  8  0  0  4  8  8 12  8  8  0  0
 0  0  0  8  0  0  0  0  0  8  8  8  0  8  0  8  8  0  8  8  8  0  0  8  8  8  8  8  8  0  8  8  0  0
 0  0  0  0  8  0  0  0  0  0  0  0  8  8  8  0  0  8  8  8  0  8  0  0  0  0  8  8  0  8  8  0  0  0
 0  0  0  0  0  8  0  0  0  8  0  0  8  8  8  0  8  0  0  0  8  8  8  8  8  0  0  8  0  8  0  8  0  0
 0  0  0  0  0  0  8  0  0  8  8  0  0  0  8  8  0  0  8  0  8  8  0  0  8  0  8  0  0  8  8  0  8  0
 0  0  0  0  0  0  0  8  0  0  8  0  0  8  0  0  0  0  8  8  8  8  8  8  0  8  0  8  8  0  0  0  8  0
 0  0  0  0  0  0  0  0  8  0  0  8  8  0  0  8  0  8  8  0  8  0  8  0  8  8  8  8  0  8  8  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+39x^24+172x^26+32x^27+316x^28+96x^29+616x^30+832x^31+1712x^32+2112x^33+4500x^34+2080x^35+1726x^36+864x^37+700x^38+128x^39+257x^40+144x^42+36x^44+12x^46+7x^48+2x^52

The gray image is a code over GF(2) with n=272, k=14 and d=96.
This code was found by Heurico 1.16 in 2.66 seconds.