The generator matrix

 1  0  1  1  1  0  X  1  1  1
 0  1  1  0 X+1  1  0  0  0  0
 0  0  X X+2  0 X+2  X  0  0  0
 0  0  0  2  0  0  0  0  2  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  0
 0  0  0  0  0  0  0  2  2  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+68x^4+232x^6+192x^7+862x^8+1856x^9+1784x^10+1856x^11+820x^12+192x^13+280x^14+41x^16+8x^18

The gray image is a code over GF(2) with n=40, k=13 and d=8.
This code was found by Heurico 1.16 in 0.0458 seconds.