The generator matrix

 1  1  1  1  X  0  1  1  X  1
 0  X  0  X  0  0  2  X  X  0
 0  0  X  X  X  X  2 X+2  X  0
 0  0  0  2  0  2  2  0  0  0
 0  0  0  0  2  2  0  0  2  0

generates a code of length 10 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+20x^6+20x^7+63x^8+108x^9+88x^10+108x^11+63x^12+20x^13+20x^14+1x^20

The gray image is a code over GF(2) with n=40, k=9 and d=12.
This code was found by Heurico 1.16 in 0.00118 seconds.