The generator matrix

 1  0  0  0  0  1  1  1  1 X+2  1
 0  1  0  0  0  2 X+1  X  1  1  2
 0  0  1  0  0 X+2  1 X+1  X X+1  2
 0  0  0  1  0 X+1  X  3  1 X+1  2
 0  0  0  0  1  1 X+1  2  X X+1  X

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+112x^6+504x^7+1190x^8+4648x^9+4820x^10+10160x^11+4896x^12+4688x^13+1144x^14+472x^15+121x^16+8x^17+4x^18

The gray image is a code over GF(2) with n=44, k=15 and d=12.
This code was found by Heurico 1.13 in 0.529 seconds.