The generator matrix

 1  0  1  1  1 2X  1
 0  1 X+1 X+2 2X+3  1 2X
 0  0 2X+2  2 2X 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+42x^5+226x^6+494x^7+215x^8+38x^9+6x^10+2x^11

The gray image is a code over GF(2) with n=56, k=10 and d=20.
This code was found by Heurico 1.16 in 2.1e-008 seconds.