The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  4  8  1  2  1  1  1  4  1  2  2
 0 12  0  0  0  4 12  4  0  8  4 12  0  8 12  4  0  8  4  8  8  4  4  8 12  4 12  4  4  0  0  0
 0  0 12  0  4  4 12  0  0  0  4  8  4  4  0 12  8  0 12  0 12  4  4 12  8  8  4  4  4  4  4  8
 0  0  0 12  4  0 12  4  0  4 12  8 12  0  4  8  4  0  8  4  4  0  8  8  0 12  0  0  0 12 12  8
 0  0  0  0  8  0  0  0  8  0  8  8  0  0  0  8  0  8  8  0  0  8  0  8  8  0  0  8  0  8  0  0
 0  0  0  0  0  8  0  0  8  8  8  0  8  0  8  8  8  0  8  0  0  0  8  8  8  0  8  0  0  8  8  8
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  8  8  0  8  0  0  8  8  8  8  0  8  0  8  8  0
 0  0  0  0  0  0  0  8  8  8  0  8  0  0  0  8  0  8  0  0  8  0  0  0  8  8  8  8  8  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+157x^24+324x^26+16x^27+674x^28+144x^29+2170x^30+2912x^31+3586x^32+2912x^33+2178x^34+144x^35+714x^36+16x^37+286x^38+101x^40+34x^42+12x^44+3x^48

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 2.68 seconds.