The generator matrix

 1  0  1  1  1  0  X  1  1  1
 0  1  1  0  1  1  0  2  2  0
 0  0  X  0  0  0  X  0  2  0
 0  0  0  X  0  0  X  2  2  0
 0  0  0  0  X  0  X  2  0  0
 0  0  0  0  0  X  X  X X+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+79x^4+44x^5+380x^6+764x^7+1583x^8+3288x^9+4110x^10+3288x^11+1569x^12+764x^13+400x^14+44x^15+64x^16+6x^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 0.176 seconds.