The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+52x^2+136x^3+407x^4+888x^5+5224x^6+888x^7+407x^8+136x^9+52x^10+1x^12

The gray image is a code over GF(2) with n=48, k=13 and d=8.
This code was found by Heurico 1.16 in 0.00789 seconds.