The generator matrix

 1  0  1  1  1 12  1  1  2 14  1  1  1  8 10  1  1  1  8  1  2  1  1  2  1  1  2  1  0  2  2  1
 0  1  1 12 11  1  2  7  1  1 13  6  3  1  1  4 14  9  1 11  1  4 14 12  7  2  1  5  0  4  4  0
 0  0  2  6  4  6  2 14  2  4  4  0  0 12  6  2  4  6  2  2  4  4  2  6  4 10 12  8  2  2  4  0
 0  0  0  8  0  0  0  0  0  8  8  8  0  8  8  0  0  8  0  0  8  0  0  0  8  0  8  0  8  8  0  0
 0  0  0  0  8  0  0  0  0  0  8  0  8  0  0  8  8  0  8  8  8  0  8  0  8  0  0  8  0  8  8  0
 0  0  0  0  0  8  0  0  8  0  0  8  0  8  0  8  8  8  8  8  8  0  0  0  0  8  0  8  0  0  0  0
 0  0  0  0  0  0  8  0  0  8  8  8  0  8  8  8  8  0  0  8  0  8  0  8  0  0  8  8  0  8  0  8
 0  0  0  0  0  0  0  8  8  0  0  8  8  8  8  8  8  0  0  0  8  8  0  8  8  8  8  8  8  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+47x^24+118x^25+341x^26+696x^27+1750x^28+4098x^29+8080x^30+10430x^31+14361x^32+10478x^33+8146x^34+4126x^35+1716x^36+646x^37+312x^38+106x^39+31x^40+20x^41+17x^42+2x^43+14x^44

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 16.9 seconds.