The generator matrix

 1  1  1  1  1  1  2  1
 0  2  0  0  0  0  2  0
 0  0  2  0  0  0  2  0
 0  0  0  2  0  0  2  0
 0  0  0  0  2  0  2  0
 0  0  0  0  0  2  2  0

generates a code of length 8 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+15x^4+6x^6+32x^7+15x^8+32x^9+20x^10+1x^12+6x^14

The gray image is a code over GF(2) with n=16, k=7 and d=4.
This code was found by Heurico 1.16 in 0.000204 seconds.