The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1
 0 12  0  0  0  0  0  0  0  0  8 12 12  4  8  0  0 12  4  4  4  8 12 12  8 12  4  4  0  8  4  8
 0  0 12  0  0  0  0  0  0  0 12 12  4  8  4  8 12  4  0  4  8  0  0 12  8  4  8  0 12 12  8 12
 0  0  0 12  0  0  8 12 12  4  4  8  4  4 12  0  0  4  4  8  4  0  0  8 12  0 12 12  8 12 12  0
 0  0  0  0 12  0 12 12  4  8  0  0  0  0  8  0 12 12 12  0  4 12  8  8 12 12  8  0  4  4 12  4
 0  0  0  0  0 12  4  8  4  4  0  0  0  0  4  8  0  8 12 12  8  0  8  0 12  4 12 12 12 12 12  4

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

Homogenous weight enumerator: w(x)=1x^0+73x^24+124x^25+164x^26+248x^27+297x^28+294x^29+325x^30+1384x^31+10544x^32+1374x^33+360x^34+312x^35+279x^36+242x^37+198x^38+104x^39+38x^40+14x^41+8x^42+1x^62

The gray image is a code over GF(2) with n=256, k=14 and d=96.
This code was found by Heurico 1.16 in 2.65 seconds.