The generator matrix

 1  0  1  1  1  4  1
 0  1  1  0  3  1  0
 0  0  2  0  2  4  0
 0  0  0  2  2  6  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+266x^4+1304x^5+5877x^6+17772x^7+5877x^8+1304x^9+266x^10+50x^11+1x^14

The gray image is a code over GF(2) with n=56, k=15 and d=12.
This code was found by Heurico 1.16 in 0.132 seconds.