The generator matrix

 1  1  1  1  2 12  1
 0  2  0  2 10  2  0
 0  0  2  2  6  6  0
 0  0  0  8  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+28x^4+82x^5+516x^6+798x^7+513x^8+78x^9+28x^10+2x^11+2x^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 0.00216 seconds.