The generator matrix

 1  0  0  1  1  1 X+2  1  1  2
 0  1  0  1  0 X+3  1  X  3  1
 0  0  1  1  1  0  1  1 X+1  X
 0  0  0  X  0  0  2 X+2 X+2 X+2
 0  0  0  0  X X+2  X X+2 X+2  X

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+152x^6+192x^7+1162x^8+1344x^9+2480x^10+1344x^11+1192x^12+192x^13+120x^14+13x^16

The gray image is a code over GF(2) with n=40, k=13 and d=12.
This code was found by Heurico 1.16 in 0.26 seconds.