The generator matrix

 1  1  1  1  2  0
 0  X  0  X  X  X
 0  0  X  X 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+74x^4+168x^5+552x^6+144x^7+77x^8+8x^9

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 0.016 seconds.