The generator matrix

 1  0  0  1  1  1  0  1  1  X  X
 0  1  0  1  X X+3  1  0 X+2  2  0
 0  0  1  1  1  0 X+3  X  0  0  X
 0  0  0  X  0 X+2 X+2  X  0  X  X
 0  0  0  0  2  0  0  2  2  0  0
 0  0  0  0  0  2  0  2  0  2  0
 0  0  0  0  0  0  2  2  2  2  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+143x^6+176x^7+1157x^8+1472x^9+3815x^10+2848x^11+3827x^12+1472x^13+1157x^14+176x^15+134x^16+5x^18+1x^20

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 6.85 seconds.