The generator matrix

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

generates a code of length 7 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+8x^4+40x^6+160x^7+37x^8+8x^10+2x^12

The gray image is a code over GF(2) with n=56, k=8 and d=16.
This code was found by Heurico 1.16 in 0.000322 seconds.