The generator matrix

 1  0  1  2  1  1
 0  1 11  0  0  0
 0  0 12 12  0  0
 0  0  0  8  0  0
 0  0  0  0  8  0
 0  0  0  0  0  8

generates a code of length 6 over Z16 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+42x^2+48x^3+271x^4+1360x^5+4748x^6+1360x^7+271x^8+48x^9+42x^10+1x^12

The gray image is a code over GF(2) with n=48, k=13 and d=8.
This code was found by Heurico 1.16 in 0.00412 seconds.