The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+18x^4+16x^5+13x^6+32x^7+13x^8+16x^9+18x^10+1x^14

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 0.000184 seconds.