The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+88x^3+583x^4+2984x^5+9072x^6+2984x^7+583x^8+88x^9+1x^12

The gray image is a code over GF(2) with n=48, k=14 and d=12.
This code was found by Heurico 1.16 in 0.062 seconds.