The generator matrix

 1  0  1  1  1 12
 0  1  1  0 11  1
 0  0  2  6  0  2
 0  0  0 12 12 12

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

Homogenous weight enumerator: w(x)=1x^0+32x^3+279x^4+1632x^5+4304x^6+1632x^7+279x^8+32x^9+1x^12

The gray image is a code over GF(2) with n=48, k=13 and d=12.
This code was found by Heurico 1.16 in 0.00871 seconds.