The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+52x^2+106x^3+254x^4+408x^5+2253x^6+10236x^7+2253x^8+408x^9+254x^10+106x^11+52x^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 0.0237 seconds.