The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+10x^9+31x^10+48x^11+30x^12+2x^13+1x^14+4x^15+1x^20

The gray image is a code over GF(2) with n=44, k=7 and d=18.
This code was found by Heurico 1.16 in 0.000449 seconds.