The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  4  2  1  1  4  0  2  2  2 12  0  1  8  4  0  2  1  1  1
 0  2  0  0  0  2  6 14  8 12 10 10  4  0 10  2  6  2  4 14 12 10  2 12  0  8  2  2  0  0 10  0
 0  0  2  0  2  2  2  0  0  4  6  2  6 12  8  0  4 14  2  4 14  2 14  2  6  0  2  2  6  8  6  0
 0  0  0  2  2  0  2  2  4  2  6  4 10  2  0  4 14  2  4 14  6 10  0 10 10  2 14 12  4 10  8  0
 0  0  0  0  8  0  0  8  0  8  8  8  0  8  8  0  0  8  0  0  0  8  0  8  0  8  0  8  0  8  8  0
 0  0  0  0  0  8  0  0  8  8  8  8  8  8  8  0  0  8  8  8  0  0  8  0  8  0  0  8  0  0  0  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  8  8  8  0  8  8  8  0  8  0  0  0

generates a code of length 32 over Z16 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+74x^24+210x^25+848x^26+1032x^27+2708x^28+3840x^29+8402x^30+8980x^31+12762x^32+9828x^33+8418x^34+3588x^35+2886x^36+944x^37+614x^38+220x^39+122x^40+26x^41+22x^42+4x^43+6x^44+1x^48

The gray image is a code over GF(2) with n=256, k=16 and d=96.
This code was found by Heurico 1.16 in 24.9 seconds.