The generator matrix

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

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+78x^6+96x^7+79x^8+2x^10

The gray image is a code over GF(2) with n=56, k=8 and d=24.
This code was found by Heurico 1.16 in -3.24e-008 seconds.