The generator matrix

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

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+47x^6+264x^7+696x^8+1892x^9+3301x^10+3856x^11+3468x^12+1960x^13+617x^14+200x^15+59x^16+20x^17+3x^18

The gray image is a code over GF(2) with n=44, k=14 and d=12.
This code was found by Heurico 1.13 in 0.137 seconds.