The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+165x^24+328x^26+945x^28+512x^29+2096x^30+1536x^31+5203x^32+1536x^33+2128x^34+512x^35+962x^36+304x^38+129x^40+8x^42+13x^44+6x^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 2.67 seconds.