The generator matrix

 1  1  1  1  1  1  X  X  1  1  1
 0  X  0  0  0  0  0  X  2  0  0
 0  0  X  0  0  0  0  X X+2  2  0
 0  0  0  X  0  0  X  0  X X+2  0
 0  0  0  0  X  0  X  0  0  2  0
 0  0  0  0  0  X  X  0  2  X  0
 0  0  0  0  0  0  2  2  0  0  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+22x^4+112x^5+199x^6+336x^7+664x^8+1488x^9+3210x^10+4320x^11+3210x^12+1488x^13+664x^14+336x^15+199x^16+112x^17+22x^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 0.243 seconds.