The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+22x^3+82x^4+330x^5+1180x^6+330x^7+77x^8+22x^9+4x^10

The gray image is a code over GF(2) with n=48, k=11 and d=12.
This code was found by Heurico 1.16 in -6.48e-008 seconds.