The generator matrix

 1  0  1  1  1  0  1  0  1  1  1
 0  1  1  0  1  1  0  1 X+3 X+2  X
 0  0  X  0  0  0  0 X+2  X  X  2
 0  0  0  X  0  0  X X+2  2 X+2  2
 0  0  0  0  X  0  X  2 X+2  X  0
 0  0  0  0  0  X  2  0 X+2  X X+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+192x^6+40x^7+886x^8+1248x^9+4028x^10+3568x^11+4064x^12+1248x^13+888x^14+40x^15+169x^16+12x^18

The gray image is a code over GF(2) with n=44, k=14 and d=12.
This code was found by Heurico 1.16 in 50 seconds.