The generator matrix

 1  1  1  1  2  2
 0  2  0  6  6 14
 0  0 12  0  8 12
 0  0  0  8  8  0

generates a code of length 6 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+70x^4+192x^5+500x^6+192x^7+65x^8+4x^10

The gray image is a code over GF(2) with n=48, k=10 and d=16.
This code was found by Heurico 1.16 in 0.000842 seconds.