The generator matrix

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

generates a code of length 32 over Z16 who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+56x^25+131x^26+168x^27+227x^28+378x^29+829x^30+1438x^31+1744x^32+1472x^33+855x^34+382x^35+159x^36+132x^37+95x^38+58x^39+43x^40+8x^41+10x^42+2x^43+2x^44+2x^45

The gray image is a code over GF(2) with n=256, k=13 and d=100.
This code was found by Heurico 1.16 in 2.83 seconds.