The generator matrix

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

generates a code of length 7 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+45x^4+32x^5+72x^6+704x^7+107x^8+32x^9+24x^10+7x^12

The gray image is a code over GF(2) with n=56, k=10 and d=16.
This code was found by Heurico 1.16 in 0.000825 seconds.