The generator matrix

 1  1  1  1  1  1  1  1  1  1  2  0  1  1  2 12  1  1  2  1  1  1  0  1  1  2  1  0  0  2  1  1  1  1
 0  2 12  6  0  6 12 10  0  6  6  2 10 12 10  2  6  0  6 12 10 10  2  0 12 10  6  2  2  6  6  6  6  0
 0  0  8  0  0  0  0  0  0  0  0  0  0  8  8  0  8  0  0  0  8  8  0  0  8  8  8  8  8  0  8  0  8  0
 0  0  0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  0  8  8  8  0  0  8  0  8  8
 0  0  0  0  8  0  0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  0  0  8  8  8  8  0  0  0  0  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  8  0  8  0  8  0  8  8  0  8  8  0  0  0  0  8  8  8  8  0  0  8
 0  0  0  0  0  0  8  0  0  0  8  0  0  8  0  8  8  0  8  8  0  8  0  8  0  8  8  8  0  0  8  8  8  0
 0  0  0  0  0  0  0  8  0  0  8  0  8  8  8  0  0  8  0  8  8  0  0  8  8  8  0  8  8  8  0  8  8  0
 0  0  0  0  0  0  0  0  8  0  8  8  0  0  0  0  0  0  0  0  8  0  0  8  8  8  8  0  8  8  8  8  0  8
 0  0  0  0  0  0  0  0  0  8  8  8  0  0  8  8  8  8  0  8  0  0  8  8  8  8  8  8  0  8  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+49x^24+8x^25+104x^26+72x^27+238x^28+448x^29+906x^30+2112x^31+3291x^32+6576x^33+5152x^34+6576x^35+3306x^36+2112x^37+916x^38+448x^39+237x^40+72x^41+72x^42+8x^43+39x^44+18x^46+6x^48+1x^60

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 7.48 seconds.