The generator matrix

 1  0  1  1  1  2  1  1  1  0
 0  1  1  0  1  1 X+3 X+1  1  0
 0  0  X  0  0  0  X  X X+2  2
 0  0  0  X  0  X  X X+2  2  X
 0  0  0  0  X  2 X+2  0 X+2  2

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+64x^6+288x^7+226x^8+1152x^9+448x^10+1472x^11+216x^12+128x^13+64x^14+32x^15+5x^16

The gray image is a code over GF(2) with n=40, k=12 and d=12.
This code was found by Heurico 1.16 in 0.0289 seconds.