The generator matrix

 1  1  1  1  2  2  2  1  1
 0  2  0 14  6  6  0  0  0
 0  0 12  4  0 12 12  0  0
 0  0  0  8  0  0  0  0  8
 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

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

Homogenous weight enumerator: w(x)=1x^0+76x^4+456x^6+640x^7+3598x^8+6912x^9+3472x^10+640x^11+540x^12+40x^14+9x^16

The gray image is a code over GF(2) with n=72, k=14 and d=16.
This code was found by Heurico 1.16 in 0.0832 seconds.