The generator matrix

 1  0  1  1  1  0  1  1  X  1
 0  1  1  0  1  1 X+1 X+1  0  0
 0  0  X  0  0  0  0  X  2  0
 0  0  0  X  0 X+2  X  X  2  0
 0  0  0  0  X  0  X  0  2  0
 0  0  0  0  0  2  0  2  2  0
 0  0  0  0  0  0  2  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+83x^4+58x^5+397x^6+524x^7+2117x^8+2510x^9+5053x^10+2440x^11+2089x^12+566x^13+431x^14+44x^15+62x^16+2x^17+7x^18

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 0.169 seconds.