The generator matrix

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

generates a code of length 6 over Z16 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+90x^2+192x^3+1551x^4+2880x^5+23340x^6+2880x^7+1551x^8+192x^9+90x^10+1x^12

The gray image is a code over GF(2) with n=48, k=15 and d=8.
This code was found by Heurico 1.16 in 0.0975 seconds.