The generator matrix

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

generates a code of length 7 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+14x^5+34x^6+38x^7+23x^8+10x^9+6x^10+2x^11

The gray image is a code over GF(2) with n=28, k=7 and d=10.
This code was found by Heurico 1.16 in 0.000177 seconds.