The generator matrix
1 0 1 1 1 0 X 1 1 X 1
0 1 1 0 X+1 1 0 0 0 0 0
0 0 X X+2 0 X+2 X 0 0 0 0
0 0 0 2 0 0 0 0 0 2 0
0 0 0 0 2 0 0 0 0 2 0
0 0 0 0 0 2 0 0 0 2 0
0 0 0 0 0 0 2 0 0 2 0
0 0 0 0 0 0 0 2 0 2 0
0 0 0 0 0 0 0 0 2 2 0
generates a code of length 11 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+76x^4+273x^6+128x^7+886x^8+1792x^9+2860x^10+4352x^11+2860x^12+1792x^13+886x^14+128x^15+273x^16+76x^18+1x^22
The gray image is a code over GF(2) with n=44, k=14 and d=8.
This code was found by Heurico 1.16 in 0.164 seconds.