The generator matrix

 1  1  1  1  2  2  1
 0  2  0  0  2  0  0
 0  0  2  0  2  0  0
 0  0  0  2  2  0  0
 0  0  0  0  4 12  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+93x^2+340x^3+1411x^4+3440x^5+10783x^6+33400x^7+10783x^8+3440x^9+1411x^10+340x^11+93x^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 0.36 seconds.