The generator matrix

 1  0  1  1  1  1
 0  1 11  0  0  0
 0  0 12  0  4  0
 0  0  0 12  4  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+112x^3+263x^4+1168x^5+5000x^6+1168x^7+263x^8+112x^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 0.00576 seconds.