The generator matrix

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

generates a code of length 10 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+92x^4+560x^6+3046x^8+8992x^10+3036x^12+560x^14+97x^16

The gray image is a code over GF(2) with n=40, k=14 and d=8.
This code was found by Heurico 1.16 in 0.236 seconds.