The generator matrix

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

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+52x^5+169x^6+620x^7+1988x^8+2888x^9+4895x^10+2968x^11+2004x^12+580x^13+151x^14+60x^15+7x^16+1x^18

The gray image is a code over GF(2) with n=40, k=14 and d=10.
This code was found by Heurico 1.13 in 0.0686 seconds.