The generator matrix

 1  1  1  1  1  1  1
 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  0  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+19x^2+81x^4+96x^5+155x^6+1344x^7+155x^8+96x^9+81x^10+19x^12+1x^14

The gray image is a code over GF(2) with n=28, k=11 and d=4.
This code was found by Heurico 1.16 in 0.00178 seconds.