The generator matrix

 1  1  1  1  1  1  1
 0 12  0  0  0  4  0
 0  0 12  0  0  4  0
 0  0  0 12  0  4  0
 0  0  0  0 12  4  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+45x^2+20x^3+211x^4+240x^5+255x^6+6648x^7+255x^8+240x^9+211x^10+20x^11+45x^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 0.00861 seconds.