The generator matrix

 1  1  1  1  1  X  1
 0  X  0  0  0  2  X
 0  0  X  0  X  2  2
 0  0  0  X  X X+2 X+2
 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 4.

Homogenous weight enumerator: w(x)=1x^0+77x^4+296x^6+256x^7+331x^8+56x^10+7x^12

The gray image is a code over GF(2) with n=28, k=10 and d=8.
This code was found by Heurico 1.16 in 0.00624 seconds.