The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+29x^2+131x^4+607x^6+2560x^7+607x^8+131x^10+29x^12+1x^14

The gray image is a code over GF(2) with n=56, k=12 and d=8.
This code was found by Heurico 1.16 in 0.00288 seconds.