The generator matrix

 1  1  1  1  1  1
 0  2  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+16x^1+106x^2+400x^3+975x^4+2656x^5+24460x^6+2656x^7+975x^8+400x^9+106x^10+16x^11+1x^12

The gray image is a code over GF(2) with n=48, k=15 and d=4.
This code was found by Heurico 1.16 in 0.0591 seconds.