The generator matrix

 1  1  1  1  1  1
 0 12  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+12x^1+66x^2+220x^3+495x^4+792x^5+13212x^6+792x^7+495x^8+220x^9+66x^10+12x^11+1x^12

The gray image is a code over GF(2) with n=48, k=14 and d=4.
This code was found by Heurico 1.16 in 0.0193 seconds.