The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+40x^7+362x^8+480x^9+480x^10+1008x^11+1096x^12+480x^13+32x^14+40x^15+77x^16

The gray image is a code over GF(2) with n=44, k=12 and d=14.
This code was found by Heurico 1.16 in 7.19 seconds.