The generator matrix
1 1 X 1 1
0 2 0 0 2
0 0 2 0 2
0 0 0 2 2
generates a code of length 5 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+18x^4+96x^5+8x^6+5x^8
The gray image is a code over GF(2) with n=40, k=7 and d=16.
This code was found by Heurico 1.16 in 3.62e-008 seconds.