The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+188x^6+642x^8+384x^9+2228x^10+1280x^11+2264x^12+384x^13+644x^14+165x^16+12x^18

The gray image is a code over GF(2) with n=44, k=13 and d=12.
This code was found by Heurico 1.16 in 17.8 seconds.