The generator matrix

 1  1  1  2  1  2
 0  2  0  2 14  0
 0  0 12  0  4  4
 0  0  0  4  8  4

generates a code of length 6 over Z16 who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+24x^3+103x^4+360x^5+1072x^6+360x^7+103x^8+24x^9+1x^12

The gray image is a code over GF(2) with n=48, k=11 and d=12.
This code was found by Heurico 1.16 in 0.000985 seconds.