The generator matrix

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

generates a code of length 10 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+26x^10+5x^12

The gray image is a code over GF(2) with n=80, k=5 and d=40.
This code was found by Heurico 1.16 in 3.81e-009 seconds.