The generator matrix

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

generates a code of length 10 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+91x^8+120x^9+136x^10+48x^11+90x^12+24x^13+2x^16

The gray image is a code over GF(2) with n=40, k=9 and d=16.
This code was found by Heurico 1.16 in 0.00495 seconds.