The generator matrix

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

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+26x^4+32x^5+37x^6+320x^7+37x^8+32x^9+26x^10+1x^14

The gray image is a code over GF(2) with n=28, k=9 and d=8.
This code was found by Heurico 1.16 in 0.000467 seconds.