The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+69x^24+308x^25+618x^26+1438x^27+2477x^28+4842x^29+7100x^30+10248x^31+11124x^32+10438x^33+7302x^34+4834x^35+2407x^36+1344x^37+520x^38+308x^39+110x^40+26x^41+12x^42+4x^43+4x^44+2x^45

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 25.9 seconds.