The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+186x^8+192x^9+288x^10+640x^11+424x^12+192x^13+96x^14+29x^16

The gray image is a code over GF(2) with n=44, k=11 and d=16.
This code was found by Heurico 1.16 in 2.87 seconds.