The generator matrix

 1  0  0  1  1  1  1  1  1  1
 0  1  0  1  0 X+3  2 X+1 X+1  0
 0  0  1  1  1  0  X  0 X+2  0
 0  0  0  X  0  0  X  2  X X+2
 0  0  0  0  X X+2  X  2  0  X
 0  0  0  0  0  2  0  2  2  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+48x^5+216x^6+628x^7+1674x^8+3412x^9+4400x^10+3432x^11+1704x^12+632x^13+184x^14+36x^15+13x^16+4x^17

The gray image is a code over GF(2) with n=40, k=14 and d=10.
This code was found by Heurico 1.16 in 15.1 seconds.