The generator matrix

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

generates a code of length 7 over Z4[X]/(X^3+2,2X) 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 -6.48e-008 seconds.