The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  0  0  2  1  2  2  1  2  1  2  1  1  8 12  0  1  2  1  1  1
 0  2  0  2  0  0  6 14  0 12  6  2  2  4 10 10 12  6  2  2  2 14 12  0 12  4  8  8 10  4  6  0
 0  0  2  2  0 14  6  0  4  2  0  6  8  2  6 14 10  8 12  6  2 10  8 12  2  2  2  8  2 14  8  0
 0  0  0  4 12  4  0  4 12  4  8  4  0  4  8  8  0  0  4  4  0  0  8  0  8  4  0  4 12  4  8  0
 0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  0  8  8  0  0  0  8  0  8  8  8  0  0  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  0  8  8  0  8  8  8  0  0  0  8  8  8  0  0  8  8  0  0  0
 0  0  0  0  0  0  8  0  8  8  8  0  8  8  0  8  0  0  8  8  0  0  0  8  8  0  0  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+52x^24+94x^25+340x^26+556x^27+1248x^28+1838x^29+3784x^30+5100x^31+6579x^32+5366x^33+3781x^34+1832x^35+1248x^36+434x^37+272x^38+124x^39+88x^40+12x^41+14x^42+4x^43+1x^50

The gray image is a code over GF(2) with n=256, k=15 and d=96.
This code was found by Heurico 1.16 in 6.9 seconds.