The generator matrix

 1  0  1  1  1  1 X+2  1  1  1  X
 0  1 X+1 X+2 X+1  1  1  3 X+1  3  0
 0  0  2  0  0  0  0  2  0  2  2
 0  0  0  2  0  0  2  2  0  2  0
 0  0  0  0  2  0  0  2  2  0  2
 0  0  0  0  0  2  0  2  2  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+98x^8+64x^9+272x^10+128x^11+328x^12+64x^13+48x^14+21x^16

The gray image is a code over GF(2) with n=44, k=10 and d=16.
This code was found by Heurico 1.16 in 0.511 seconds.