The generator matrix

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

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+180x^8+120x^9+578x^10+280x^11+612x^12+104x^13+156x^14+8x^15+7x^16+2x^18

The gray image is a code over GF(2) with n=44, k=11 and d=16.
This code was found by Heurico 1.11 in 0.00596 seconds.