The generator matrix

 1  1  1  1  1  1  1  1  1  1  2  0  1  1  2 12  1  2  1  0  1  1  1  2 12  1  1  1  0  2  2  1  1  1
 0  2 12  6  0  6 12 10  0  6  6  2 12 10 10  2 12  6  6  2  0  0 10 10  2  6  6 12  2  6  0  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  8  8  0  8  8  8  0  0  8  8  0  8  8  0  0  0  8  0  8  0  0  0
 0  0  0  8  0  0  0  0  0  8  0  8  8  8  0  0  8  8  0  8  0  0  8  8  8  8  0  8  8  8  8  0  0  0
 0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  0  8  8  0  8  0  0  8  8  0  0  0  8  0  0  0  0
 0  0  0  0  0  8  0  0  0  8  8  0  0  8  0  8  0  0  8  8  0  0  0  8  0  8  0  8  0  8  8  0  0  0
 0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  0  0  8  8  8  0  0  8  8  8  0  0  0  0  8  0  0  0  0
 0  0  0  0  0  0  0  8  0  0  8  8  0  8  8  8  0  0  0  8  8  0  8  0  0  8  8  0  0  0  8  0  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  0  8  8  0  8  8  0  8  8  8  0  8  8  8  8  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+75x^24+16x^25+72x^26+108x^27+85x^28+328x^29+421x^30+1144x^31+1849x^32+2488x^33+3177x^34+2528x^35+1906x^36+1144x^37+338x^38+296x^39+155x^40+120x^41+42x^42+20x^43+25x^44+41x^46+5x^50

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 2.04 seconds.