The generator matrix

 1  1  1  X 2X  1  1
 0  X  0 3X+2  X X+2 2X+2
 0  0  2 2X 2X+2 2X+2 2X+2

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

Homogenous weight enumerator: w(x)=1x^0+26x^5+130x^6+206x^7+119x^8+22x^9+6x^10+2x^11

The gray image is a code over GF(2) with n=56, k=9 and d=20.
This code was found by Heurico 1.16 in 0 seconds.