The generator matrix

 1  0  1  1  1  0  0
 0  1  1  0 X+1  1  1
 0  0  X X+2  0  0  2
 0  0  0  2  0  2  2
 0  0  0  0  2  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+42x^4+64x^5+213x^6+384x^7+213x^8+64x^9+42x^10+1x^14

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 0.000988 seconds.