The generator matrix

 1  1  2  2  1  1  1
 0  2  2  0  0  0  0
 0  0  4 12  0  0  0
 0  0  0  8  0  0  0
 0  0  0  0  8  0  0
 0  0  0  0  0  8  0
 0  0  0  0  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+27x^2+16x^3+121x^4+288x^5+1387x^6+4512x^7+1387x^8+288x^9+121x^10+16x^11+27x^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 0.00962 seconds.