The generator matrix

 1  1  2  2  1  1
 0  2  2  0  0  0
 0  0  4 12  0  0
 0  0  0  8  0  0
 0  0  0  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+24x^2+16x^3+103x^4+304x^5+1152x^6+304x^7+103x^8+16x^9+24x^10+1x^12

The gray image is a code over GF(2) with n=48, k=11 and d=8.
This code was found by Heurico 1.16 in 0.000865 seconds.