The generator matrix

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

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+72x^7+266x^8+424x^9+464x^10+472x^11+240x^12+56x^13+28x^14+5x^16

The gray image is a code over GF(2) with n=40, k=11 and d=12.
This code was found by Heurico 1.16 in 0.00827 seconds.