The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+14x^5+34x^6+166x^7+23x^8+10x^9+6x^10+2x^11

The gray image is a code over GF(2) with n=56, k=8 and d=20.
This code was found by Heurico 1.16 in 3.81e-009 seconds.