The generator matrix

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

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+68x^4+224x^6+638x^8+384x^9+2120x^10+1280x^11+2204x^12+384x^13+560x^14+281x^16+40x^18+8x^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 0.044 seconds.