The generator matrix

 1  1  1  1  1  1  1
 0  2  0  2 2X 2X+2 2X
 0  0 2X 2X 2X 2X  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+7x^6+112x^7+7x^8+1x^14

The gray image is a code over GF(2) with n=56, k=7 and d=24.
This code was found by Heurico 1.16 in -3.24e-008 seconds.