The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+8x^11+5x^12+2x^14

The gray image is a code over GF(2) with n=44, k=4 and d=22.
This code was found by Heurico 1.16 in 0.000259 seconds.