The generator matrix

 1  0  1  1  1  6  1  1  8  1 14  1  1  1  6  2  1  1  0  1  1 14  1  1  1  4  1  2  2  1  1  2
 0  1 11  6  5  1  0  3  1 13  1  6  3  8  1  1  9  4  1  7  2  1 14  8 11  1  3  4  4  6  2  0
 0  0 12  0  0  4  4  4  0  0 12  0  8  8  0 12  8  4 12  8  8  0 12 12  0 12 12  4  0  4  8  0
 0  0  0 12  0  4  4  4  4  4  8  8  0  4  0  8  0  0 12  4  4 12  8  0  4  8 12  0  4 12 12  0
 0  0  0  0  8  0  0  0  0  0  8  8  0  8  0  0  8  0  8  0  8  8  8  0  8  0  8  0  0  0  8  0
 0  0  0  0  0  8  0  0  0  8  0  0  8  8  8  0  8  0  0  0  8  8  0  0  8  8  0  0  0  8  8  0
 0  0  0  0  0  0  8  0  0  0  0  8  0  0  8  8  8  8  0  8  0  8  8  0  0  8  0  8  8  0  8  8
 0  0  0  0  0  0  0  8  8  0  0  8  8  8  8  0  8  0  0  0  0  0  8  8  8  0  8  8  0  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+165x^24+24x^25+416x^26+508x^27+1752x^28+3604x^29+7164x^30+13324x^31+11659x^32+13268x^33+7260x^34+3508x^35+1780x^36+508x^37+372x^38+68x^39+117x^40+4x^41+20x^42+12x^44+2x^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 18.4 seconds.