The generator matrix

 1  0  1  1  1  0  X  1  1  1  1
 0  1  1  0 X+1  1  X  X  2  X  2
 0  0  X X+2  0 X+2  X  X  X  X  X
 0  0  0  2  0  0  0  0  2  2  0
 0  0  0  0  2  0  0  2  2  0  0
 0  0  0  0  0  2  0  2  2  0  2
 0  0  0  0  0  0  2  2  2  2  2

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+43x^6+48x^7+149x^8+640x^9+307x^10+1696x^11+339x^12+640x^13+153x^14+48x^15+22x^16+9x^18+1x^20

The gray image is a code over GF(2) with n=44, k=12 and d=12.
This code was found by Heurico 1.16 in 0.0188 seconds.