The generator matrix

 1  0  1  1  1 X+2  1  1  1  1  0
 0  1  1 X+2 X+3  1  2  X X+1  0  1
 0  0  X  0 X+2  2  X X+2  0  0  2
 0  0  0  2  0  2  0  2  0  2  0
 0  0  0  0  2  0  2  0  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+72x^8+96x^9+248x^10+192x^11+252x^12+96x^13+56x^14+11x^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 0.00676 seconds.