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.