The generator matrix

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

generates a code of length 7 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+21x^4+32x^6+67x^8+7x^12

The gray image is a code over GF(2) with n=14, k=7 and d=4.
This code was found by Heurico 1.16 in 0.000181 seconds.