The generator matrix
1 0 0 0 1
0 1 0 0 X+1
0 0 1 0 1
0 0 0 1 1
0 0 0 0 2
generates a code of length 5 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+285x^2+3360x^3+24930x^4+73920x^5+24930x^6+3360x^7+285x^8+1x^10
The gray image is a code over GF(2) with n=40, k=17 and d=8.
This code was found by Heurico 1.16 in 1.97 seconds.