The generator matrix

 1  1  1  1  1  1  1  X  1  2  X
 0  X  0  0  0  0  2 X+2  X  X  2
 0  0  X  0  0  2 X+2  X  2 X+2  0
 0  0  0  X  0 X+2  X  2  X X+2  X
 0  0  0  0  X  X  0 X+2  2 X+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+362x^8+480x^10+1096x^12+32x^14+77x^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 0.282 seconds.