The generator matrix

 1  0  0  1  1  1  X  1  1  1  1
 0  1  0  1 X+2 X+3  1  2  0 X+2  0
 0  0  1  1 X+3 X+2  1  X  0  0  0
 0  0  0  2  0  0  2  0  0  2  0
 0  0  0  0  2  0  2  2  0  2  0
 0  0  0  0  0  2  2  2  2  0  0

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+68x^6+294x^8+384x^9+656x^10+1280x^11+672x^12+384x^13+292x^14+57x^16+8x^18

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 0.0174 seconds.