The generator matrix

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

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+70x^4+192x^5+500x^6+192x^7+65x^8+4x^10

The gray image is a code over GF(2) with n=48, k=10 and d=16.
This code was found by Heurico 1.16 in -6.48e-008 seconds.