The generator matrix

 1  1  1  1  1  1  1  1  1  1  2  2  1  2  1  2  2  2  2  1  1  1  1  2  1  1  1  1
 0  8  0  0  0  8  8  8  0  0  0  0  8  8  8  8  0  8  8  0  0  8  8  0  0  0  0  8
 0  0  8  0  8  8  8  0  0  0  8  8  8  0  8  0  0  8  8  8  8  0  0  0  0  0  8  8
 0  0  0  8  8  0  8  8  0  8  8  0  0  8  8  0  8  0  8  8  0  8  0  0  0  8  8  0

generates a code of length 28 over Z16 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+4x^26+116x^28+4x^30+2x^36+1x^40

The gray image is a code over GF(2) with n=224, k=7 and d=104.
This code was found by Heurico 1.16 in 0.00809 seconds.