The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+63x^4+56x^6+754x^8+512x^9+1048x^10+3072x^11+1510x^12+512x^13+424x^14+221x^16+8x^18+11x^20

The gray image is a code over GF(2) with n=44, k=13 and d=8.
This code was found by Heurico 1.16 in 0.0728 seconds.