The generator matrix

 1  1  1  1  1  1  1
 0  2  0  0  4 14  0
 0  0  2  0  6  6  0
 0  0  0  2  2  4  0
 0  0  0  0  8  0  8

generates a code of length 7 over Z16 who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+50x^3+202x^4+664x^5+1845x^6+10860x^7+1845x^8+664x^9+202x^10+50x^11+1x^14

The gray image is a code over GF(2) with n=56, k=14 and d=12.
This code was found by Heurico 1.16 in 0.0494 seconds.