The generator matrix

 1  1  1  1  1  1  1  1  X  1
 0  2  0  0  0  0  0  0  2  0
 0  0  2  0  0  0  0  0  2  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+28x^4+8x^6+70x^8+128x^9+568x^10+128x^11+28x^12+56x^14+1x^16+8x^18

The gray image is a code over GF(2) with n=40, k=10 and d=8.
This code was found by Heurico 1.16 in 0.00154 seconds.