The generator matrix

 1  1  1  1  X  X  1  1  X  1  1
 0  X  0 X+2  X  X  0  0  0  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  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+36x^4+32x^6+190x^8+128x^9+232x^10+768x^11+316x^12+128x^13+112x^14+89x^16+8x^18+8x^20

The gray image is a code over GF(2) with n=44, k=11 and d=8.
This code was found by Heurico 1.16 in 0.0043 seconds.