The generator matrix

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

generates a code of length 10 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+48x^6+206x^7+331x^8+1072x^9+773x^10+1084x^11+338x^12+192x^13+42x^14+6x^15+2x^16+1x^18

The gray image is a code over GF(2) with n=40, k=12 and d=12.
This code was found by Heurico 1.11 in 0.0122 seconds.