The generator matrix

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

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+77x^4+224x^6+434x^8+2624x^10+434x^12+224x^14+77x^16+1x^20

The gray image is a code over GF(2) with n=40, k=12 and d=8.
This code was found by Heurico 1.16 in 0.0132 seconds.