The generator matrix

 1  1  1  1  X  X
 0  X  2 3X+2 3X+2 3X+2
 0  0 2X  0  0 2X
 0  0  0 2X  0 2X
 0  0  0  0 2X 2X

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

Homogenous weight enumerator: w(x)=1x^0+87x^4+128x^5+592x^6+128x^7+87x^8+1x^12

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.