The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+8x^9+22x^10+22x^12+8x^13+2x^14+1x^16

The gray image is a code over GF(2) with n=44, k=6 and d=18.
This code was found by Heurico 1.16 in 0.000721 seconds.