The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+76x^24+280x^25+597x^26+1188x^27+2319x^28+4938x^29+6205x^30+11824x^31+10070x^32+12424x^33+6693x^34+4760x^35+2065x^36+1204x^37+493x^38+208x^39+121x^40+32x^41+26x^42+4x^43+4x^44+2x^45+2x^46

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 27.6 seconds.