The generator matrix

 1  1  1  1  2  2  1  1
 0  2  0  6  6  6  8  0
 0  0 12  0  0  4  8  0
 0  0  0 12  0  4  4  8
 0  0  0  0  8  8  8  0

generates a code of length 8 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+28x^4+50x^5+223x^6+712x^7+2057x^8+732x^9+222x^10+40x^11+26x^12+2x^13+3x^14

The gray image is a code over GF(2) with n=64, k=12 and d=16.
This code was found by Heurico 1.16 in 0.0045 seconds.