The generator matrix

 1  1  1  1  1  1  1
 0 12  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  0

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

Homogenous weight enumerator: w(x)=1x^0+28x^2+10x^3+86x^4+120x^5+141x^6+3324x^7+141x^8+120x^9+86x^10+10x^11+28x^12+1x^14

The gray image is a code over GF(2) with n=56, k=12 and d=8.
This code was found by Heurico 1.16 in 0.00347 seconds.