The generator matrix

 1  0  1  1  1  1  1
 0  1 11 14  6  8  0
 0  0 12  4  0 12  8
 0  0  0  8  8  8  0

generates a code of length 7 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+31x^4+52x^5+354x^6+1176x^7+349x^8+52x^9+30x^10+3x^12

The gray image is a code over GF(2) with n=56, k=11 and d=16.
This code was found by Heurico 1.16 in 0.00179 seconds.