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

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

Homogenous weight enumerator: w(x)=1x^0+209x^24+1632x^28+202x^32+3x^40+1x^48

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 16.2 seconds.