The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+70x^4+366x^6+1288x^8+4398x^10+4096x^11+4482x^12+1210x^14+423x^16+42x^18+8x^20

The gray image is a code over GF(2) with n=44, k=14 and d=8.
This code was found by Heurico 1.16 in 0.238 seconds.