The generator matrix

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

generates a code of length 6 over Z16 who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+24x^1+186x^2+760x^3+1935x^4+6384x^5+46956x^6+6384x^7+1935x^8+760x^9+186x^10+24x^11+1x^12

The gray image is a code over GF(2) with n=48, k=16 and d=4.
This code was found by Heurico 1.16 in 0.142 seconds.