The generator matrix

 1  1  2  1  1  1
 0 12 12  0  0  0
 0  0  8  0  0  0
 0  0  0  8  0  0
 0  0  0  0  8  0
 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+10x^2+31x^4+128x^5+684x^6+128x^7+31x^8+10x^10+1x^12

The gray image is a code over GF(2) with n=48, k=10 and d=8.
This code was found by Heurico 1.16 in 0.000298 seconds.