The generator matrix

 1  0  1  2  1  1  1
 0  1 11  0  0  0  0
 0  0 12 12  0  0  0
 0  0  0  8  0  0  0
 0  0  0  0  8  0  0
 0  0  0  0  0  8  0
 0  0  0  0  0  0  8

generates a code of length 7 over Z16 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+43x^2+48x^3+201x^4+416x^5+2827x^6+9312x^7+2827x^8+416x^9+201x^10+48x^11+43x^12+1x^14

The gray image is a code over GF(2) with n=56, k=14 and d=8.
This code was found by Heurico 1.16 in 0.0242 seconds.