The generator matrix

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

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+95x^8+112x^9+132x^10+64x^11+86x^12+16x^13+4x^14+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 1.13 in 1.07e-007 seconds.