The generator matrix

 1  0  0  1  1  1  X  1  1  1  1
 0  1  0  1  X X+1  1 X+1  1 X+3 X+1
 0  0  1  1 X+1  X  1 X+3 X+1  0  1
 0  0  0  2  0  0  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+48x^8+168x^9+152x^10+312x^11+124x^12+152x^13+56x^14+8x^15+3x^16

The gray image is a code over GF(2) with n=44, k=10 and d=16.
This code was found by Heurico 1.11 in 0.00212 seconds.