The generator matrix

 1  1  1  1  X  X  X  0  X  X
 0  X  0  X  0  X X+2  X X+2  0
 0  0  X  X  X  X  0  0  2  2
 0  0  0  2  0  0  2  0  2  0
 0  0  0  0  2  0  2  0  2  2
 0  0  0  0  0  2  2  2  0  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+55x^6+48x^7+106x^8+208x^9+187x^10+208x^11+112x^12+48x^13+45x^14+5x^16+1x^18

The gray image is a code over GF(2) with n=40, k=10 and d=12.
This code was found by Heurico 1.16 in 0.0156 seconds.