The generator matrix

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

generates a code of length 7 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+18x^6+24x^7+19x^8+2x^10

The gray image is a code over GF(2) with n=56, k=6 and d=24.
This code was found by Heurico 1.16 in 3.81e-009 seconds.