The generator matrix

 1  0  0  0  0  1  1  1  1  1  0
 0  1  0  0  0  0  1  1  X  2  1
 0  0  1  0  0 X+1 X+1  X  3  0 X+2
 0  0  0  1  0  1  X X+1 X+2  X X+3
 0  0  0  0  1  1  2  0  3 X+1  X
 0  0  0  0  0  2  0  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+247x^6+872x^7+2944x^8+7544x^9+13225x^10+15888x^11+13116x^12+7664x^13+3001x^14+776x^15+227x^16+24x^17+7x^18

The gray image is a code over GF(2) with n=44, k=16 and d=12.
This code was found by Heurico 1.13 in 10.9 seconds.