The generator matrix
1 1 1 1 X 1 X 1 X X
0 2 0 2 2 0 0 2 2 0
generates a code of length 10 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+12x^10+1x^12+2x^14
The gray image is a code over GF(2) with n=40, k=4 and d=20.
This code was found by Heurico 1.16 in 0.000204 seconds.