The generator matrix

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

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+51x^8+32x^9+88x^10+32x^11+50x^12+2x^16

The gray image is a code over GF(2) with n=40, k=8 and d=16.
This code was found by Heurico 1.16 in 0.000617 seconds.