The generator matrix

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

generates a code of length 10 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+112x^8+64x^9+168x^10+64x^11+92x^12+8x^14+3x^16

The gray image is a code over GF(2) with n=40, k=9 and d=16.
This code was found by Heurico 1.16 in 0.0277 seconds.