The generator matrix

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

generates a code of length 10 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+42x^5+105x^6+292x^7+772x^8+1710x^9+2335x^10+1720x^11+788x^12+294x^13+87x^14+36x^15+7x^16+2x^17+1x^18

The gray image is a code over GF(2) with n=40, k=13 and d=10.
This code was found by Heurico 1.16 in 1.74 seconds.