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.