The generator matrix

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

generates a code of length 9 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+23x^4+32x^6+32x^7+77x^8+704x^9+56x^10+32x^11+53x^12+8x^14+6x^16

The gray image is a code over GF(2) with n=72, k=10 and d=16.
This code was found by Heurico 1.16 in 0.00104 seconds.