The generator matrix

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

generates a code of length 7 over Z4 who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+14x^1+91x^2+364x^3+1001x^4+2002x^5+3003x^6+3432x^7+3003x^8+2002x^9+1001x^10+364x^11+91x^12+14x^13+1x^14

The gray image is a code over GF(2) with n=14, k=14 and d=1.
This code was found by Heurico 1.16 in 0.109 seconds.