The generator matrix

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

generates a code of length 14 over Z16 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+24x^14+7x^16

The gray image is a code over GF(2) with n=112, k=5 and d=56.
This code was found by Heurico 1.16 in 0.00064 seconds.