The generator matrix

 1  1  2  1  1  1  1
 0  2  2  0  0  0  0
 0  0  4  0  0  0  8
 0  0  0 12  0  0  8
 0  0  0  0 12  0  8
 0  0  0  0  0 12  8

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

Homogenous weight enumerator: w(x)=1x^0+55x^2+88x^3+469x^4+928x^5+5619x^6+18448x^7+5619x^8+928x^9+469x^10+88x^11+55x^12+1x^14

The gray image is a code over GF(2) with n=56, k=15 and d=8.
This code was found by Heurico 1.16 in 0.147 seconds.