The generator matrix

 1  0  0  1  1  1  X  1  1  1  1
 0  1  0  1 X+2 X+3  1  2  X  0  2
 0  0  1  1 X+3 X+2  1  X  X  0  X
 0  0  0  2  0  0  0  2  0  2  0
 0  0  0  0  2  0  0  2  2  0  0
 0  0  0  0  0  2  0  2  2  2  0
 0  0  0  0  0  0  2  2  0  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+74x^6+534x^8+768x^9+1430x^10+2560x^11+1456x^12+768x^13+534x^14+57x^16+10x^18

The gray image is a code over GF(2) with n=44, k=13 and d=12.
This code was found by Heurico 1.16 in 0.0634 seconds.