The generator matrix

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

generates a code of length 28 over Z16 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+200x^24+184x^26+256x^27+786x^28+256x^29+192x^30+141x^32+8x^34+22x^36+2x^40

The gray image is a code over GF(2) with n=224, k=11 and d=96.
This code was found by Heurico 1.16 in 0.762 seconds.