The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+91x^2+1001x^4+5051x^6+20480x^7+5051x^8+1001x^10+91x^12+1x^14

The gray image is a code over GF(2) with n=56, k=15 and d=8.
This code was found by Heurico 1.16 in 0.204 seconds.