The generator matrix

 1  1  1  1  1  1  1
 0  X  0  0  0  X  0
 0  0  X  0  0  X  0
 0  0  0  X  0  X  0
 0  0  0  0  X  X  0
 0  0  0  0  0  2  0
 0  0  0  0  0  0  2

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

Homogenous weight enumerator: w(x)=1x^0+47x^2+40x^3+301x^4+480x^5+675x^6+5104x^7+675x^8+480x^9+301x^10+40x^11+47x^12+1x^14

The gray image is a code over GF(2) with n=28, k=13 and d=4.
This code was found by Heurico 1.16 in 0.0303 seconds.