The generator matrix

 1  1  X  1  1  1
 0 2X  0  0 2X  0
 0  0 2X  0 2X  0
 0  0  0 2X 2X  0

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

Homogenous weight enumerator: w(x)=1x^0+6x^4+8x^5+100x^6+8x^7+1x^8+4x^10

The gray image is a code over GF(2) with n=48, k=7 and d=16.
This code was found by Heurico 1.16 in 3.62e-008 seconds.