The generator matrix

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

generates a code of length 7 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+178x^4+272x^5+845x^6+1504x^7+845x^8+272x^9+178x^10+1x^14

The gray image is a code over GF(2) with n=28, k=12 and d=8.
This code was found by Heurico 1.16 in 0.108 seconds.