The generator matrix
1 0 0 0 0 1 1 1 1 X+2 1
0 1 0 0 0 2 X+1 X 1 1 2
0 0 1 0 0 X+2 1 X+1 X X+1 2
0 0 0 1 0 X+1 X 3 1 X+1 2
0 0 0 0 1 1 X+1 2 X X+1 X
generates a code of length 11 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+112x^6+504x^7+1190x^8+4648x^9+4820x^10+10160x^11+4896x^12+4688x^13+1144x^14+472x^15+121x^16+8x^17+4x^18
The gray image is a code over GF(2) with n=44, k=15 and d=12.
This code was found by Heurico 1.13 in 0.529 seconds.