The generator matrix

 1  0  0  1  1  1  1
 0  1  0  X  3 X+2  0
 0  0  1  1 X+1  3  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+19x^4+64x^5+93x^6+162x^7+90x^8+60x^9+19x^10+2x^11+2x^12

The gray image is a code over GF(2) with n=28, k=9 and d=8.
This code was found by Heurico 1.13 in 7.44e-008 seconds.