The generator matrix

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

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+45x^8+44x^9+104x^10+8x^11+34x^12+12x^13+8x^14

The gray image is a code over GF(2) with n=40, k=8 and d=16.
This code was found by Heurico 1.16 in 0.000598 seconds.