The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+2x^10+24x^11+3x^12+1x^14+1x^18

The gray image is a code over GF(2) with n=44, k=5 and d=20.
This code was found by Heurico 1.16 in 0.000284 seconds.