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  1  1
 0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  0  0  8  0  8  8  8
 0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  8  8  8  8  8  8  0  0  0  0  8  0  8  8  0  8  0
 0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  8  0  0  8  8  0  0  0  0  0  0  8  8
 0  0  0  0  8  0  0  0  0  0  0  8  0  8  8  0  8  8  0  0  0  8  8  0  0  8  0  8  0  8  0  8
 0  0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  0  8  0  0  8  0  0  8  0  0  8  8  0  8  8
 0  0  0  0  0  0  8  0  0  0  8  0  0  0  8  8  0  0  0  0  8  8  8  8  0  0  0  8  8  8  8  0
 0  0  0  0  0  0  0  8  0  0  8  0  0  8  0  0  8  0  0  8  0  0  8  8  8  8  8  8  0  0  0  8
 0  0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  0  0  8  0  8  8  0  0  8  0  8  0  8  8  0  0
 0  0  0  0  0  0  0  0  0  8  8  8  8  0  0  8  8  0  0  8  8  0  0  8  8  0  8  0  0  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+184x^24+224x^28+7374x^32+224x^36+184x^40+1x^64

The gray image is a code over GF(2) with n=256, k=13 and d=96.
This code was found by Heurico 1.16 in 15 seconds.