The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+28x^5+89x^6+170x^7+297x^8+480x^9+1653x^10+2734x^11+1675x^12+492x^13+299x^14+166x^15+74x^16+24x^17+7x^18+2x^19+1x^20

The gray image is a code over GF(2) with n=44, k=13 and d=10.
This code was found by Heurico 1.16 in 0.0995 seconds.