The generator matrix

 1  1  1  1  1  1  X  X  1  1
 0  X  0  0  0  0  2 X+2  0 X+2
 0  0  X  0  0  0 X+2  2 X+2 X+2
 0  0  0  X  0  X  X X+2  X  0
 0  0  0  0  X  X  0  X  2  X
 0  0  0  0  0  2  2  0  0  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+36x^5+97x^6+152x^7+356x^8+828x^9+1135x^10+848x^11+372x^12+156x^13+79x^14+24x^15+7x^16+4x^17+1x^18

The gray image is a code over GF(2) with n=40, k=12 and d=10.
This code was found by Heurico 1.16 in 0.441 seconds.