The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  2  2  4  4  2  2  1  4  8  0  1  1  4  1  1
 0 12  0  0  0  0  0  0  0 12 12 12  4  4  4  4  4  4  0  8 12  8 12 12 12 12  0  8  0  4 12  4  4  0
 0  0 12  0  0  0  4 12  4  4 12  8  4  0 12  8 12  8  4  8  0 12 12  4  4  4 12  4  4 12 12  0 12  0
 0  0  0 12  0  4  4 12  0  8 12  4  8 12  4  0  8 12  4  8  8  0  0 12  4  4 12 12  0  4  0  8 12  0
 0  0  0  0 12  4  0 12  4 12  8  4  0  8 12  4  0  0  4  4  8  4  4  0  8  8  4  0  8 12 12 12  4  0
 0  0  0  0  0  8  0  0  8  8  0  8  8  8  8  8  0  8  8  0  0  8  0  8  8  0  8  8  8  8  8  0  0  0
 0  0  0  0  0  0  8  0  8  8  8  0  0  0  0  0  0  8  8  0  8  0  0  8  8  8  0  0  8  8  0  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  0  8  0  0  8  8  0  8  8  0  8  8  0  8  8  8  0  8  0  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+42x^24+102x^25+164x^26+266x^27+418x^28+596x^29+1168x^30+1946x^31+3634x^32+5274x^33+5421x^34+5284x^35+3799x^36+1970x^37+1174x^38+618x^39+378x^40+228x^41+124x^42+72x^43+46x^44+18x^45+10x^46+4x^47+1x^48+4x^49+3x^50+2x^51+1x^52

The gray image is a code over GF(2) with n=272, k=15 and d=96.
This code was found by Heurico 1.16 in 9.98 seconds.