The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+101x^2+480x^3+1067x^4+2304x^5+11887x^6+33856x^7+11887x^8+2304x^9+1067x^10+480x^11+101x^12+1x^14

The gray image is a code over GF(2) with n=56, k=16 and d=8.
This code was found by Heurico 1.16 in 0.199 seconds.