The generator matrix

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

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+26x^5+66x^6+78x^7+55x^8+22x^9+6x^10+2x^11

The gray image is a code over GF(2) with n=28, k=8 and d=10.
This code was found by Heurico 1.16 in 0.000279 seconds.