The generator matrix

 1  0  0  0  1  1  1  1  1  1
 0  1  0  0  X  1  1 X+1  1  0
 0  0  1  0 X+1  1  X X+1  X  0
 0  0  0  1  1 X+2 X+1  0  0  2
 0  0  0  0  2  0  0  2  2  2
 0  0  0  0  0  2  0  2  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+219x^6+662x^7+1594x^8+3650x^9+4051x^10+3660x^11+1600x^12+664x^13+209x^14+30x^15+5x^16+2x^17+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 1.16 in 0.207 seconds.