The generator matrix

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

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+13x^8+56x^10+43x^12+8x^14+6x^16+1x^20

The gray image is a code over GF(2) with n=44, k=7 and d=16.
This code was found by Heurico 1.16 in 0.000495 seconds.