The generator matrix

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

generates a code of length 13 over Z16 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+1x^12+22x^13+2x^14+6x^15

The gray image is a code over GF(2) with n=104, k=5 and d=48.
This code was found by Heurico 1.16 in 0.000487 seconds.