The generator matrix

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

generates a code of length 7 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+7x^6+16x^7+7x^8+1x^14

The gray image is a code over GF(2) with n=14, k=5 and d=6.
This code was found by Heurico 1.16 in 0.000133 seconds.