The generator matrix

 1  0  1  1  1 X+2  1  1  X  1
 0  1  1  0 X+1  1  X  0  2  0
 0  0  X X+2  0  0 X+2  2  X  0
 0  0  0  2  0  2  0  2  0  0
 0  0  0  0  2  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+16x^6+48x^7+97x^8+260x^9+157x^10+300x^11+94x^12+28x^13+18x^14+4x^15+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 0.00246 seconds.