The generator matrix

 1  1  2  1  1  1  1
 0  2  2  0  0  0  0
 0  0  4  0  4  0  0
 0  0  0 12  4  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+37x^2+32x^3+187x^4+96x^5+1567x^6+4352x^7+1567x^8+96x^9+187x^10+32x^11+37x^12+1x^14

The gray image is a code over GF(2) with n=56, k=13 and d=8.
This code was found by Heurico 1.16 in 0.00936 seconds.