The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+33x^8+100x^9+32x^10+196x^11+30x^12+76x^13+24x^14+12x^15+8x^16

The gray image is a code over GF(2) with n=44, k=9 and d=16.
This code was found by Heurico 1.13 in -9.54e-008 seconds.