The generator matrix

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

generates a code of length 6 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+28x^5+69x^6+28x^7+1x^8+1x^10

The gray image is a code over GF(2) with n=48, k=7 and d=20.
This code was found by Heurico 1.16 in -6.48e-008 seconds.