The generator matrix

 1  0  0  1  1  1  1  X  1  1  1
 0  1  0  1 X+2 X+3  3  1  X  X  3
 0  0  1  1  1  0 X+1 X+1  X X+1 X+2
 0  0  0  X X+2  X  2 X+2  0 X+2 X+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+158x^8+216x^9+404x^10+472x^11+449x^12+200x^13+132x^14+8x^15+7x^16+1x^20

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 0.0139 seconds.