The generator matrix

 1  1  1  1  1  1  X  1  X  1
 0  X  0  0  0  0 X+2  2  2  X
 0  0  X  0  0  2  X X+2  0  2
 0  0  0  X  0 X+2  2  X  X  X
 0  0  0  0  X  X X+2  0  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+40x^6+160x^7+194x^8+256x^9+560x^10+576x^11+184x^12+40x^14+32x^15+5x^16

The gray image is a code over GF(2) with n=40, k=11 and d=12.
This code was found by Heurico 1.16 in 0.0106 seconds.