The generator matrix

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

generates a code of length 10 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+6x^9+19x^10+3x^12+2x^13+1x^14

The gray image is a code over GF(2) with n=40, k=5 and d=18.
This code was found by Heurico 1.16 in 0.000216 seconds.