The generator matrix

 1  0  0  0  1  1  1
 0  1  0  0  X  3  0
 0  0  1  0 X+1  1  0
 0  0  0  1  1  X  0
 0  0  0  0  2  0  2

generates a code of length 7 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+50x^3+202x^4+664x^5+1845x^6+2668x^7+1845x^8+664x^9+202x^10+50x^11+1x^14

The gray image is a code over GF(2) with n=28, k=13 and d=6.
This code was found by Heurico 1.13 in 0.00219 seconds.