The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+34x^8+24x^10+128x^11+48x^12+8x^14+13x^16

The gray image is a code over GF(2) with n=44, k=8 and d=16.
This code was found by Heurico 1.16 in 0.000747 seconds.