The generator matrix

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

generates a code of length 6 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+9x^4+34x^5+173x^6+28x^7+6x^8+2x^9+3x^10

The gray image is a code over GF(2) with n=48, k=8 and d=16.
This code was found by Heurico 1.16 in 3.62e-008 seconds.