The generator matrix

 1  1  1  1  1  1  1  1  X  X  1
 0  X  0 X+2  0  2 X+2 X+2  0  2  0
 0  0  2  0  0  2  0  0  2  2  0
 0  0  0  2  0  0  0  2  2  2  0
 0  0  0  0  2  2  2  2  0  0  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+22x^8+32x^9+12x^10+128x^11+8x^12+32x^13+16x^14+1x^16+4x^18

The gray image is a code over GF(2) with n=44, k=8 and d=16.
This code was found by Heurico 1.16 in 0.000831 seconds.