The generator matrix

 1  0  0  0  0  1  1  1  1  1
 0  1  0  0  0  X  1  3 X+3  2
 0  0  1  0  0  1 X+1  X  X  0
 0  0  0  1  0  1  X X+1  0  2
 0  0  0  0  1  1  2 X+2 X+1 X+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+68x^5+393x^6+1220x^7+4036x^8+5832x^9+9567x^10+5992x^11+4052x^12+1140x^13+375x^14+84x^15+7x^16+1x^18

The gray image is a code over GF(2) with n=40, k=15 and d=10.
This code was found by Heurico 1.13 in 0.262 seconds.