The generator matrix
1 1 1 1 1
0 X^3+X^2 0 0 X^3
0 0 X^3+X^2 0 X^3
0 0 0 X^3+X^2 X^3
generates a code of length 5 over Z2[X]/(X^4) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+17x^2+24x^3+46x^4+848x^5+46x^6+24x^7+17x^8+1x^10
The gray image is a linear code over GF(2) with n=40, k=10 and d=8.
This code was found by Heurico 1.16 in -3.24e-008 seconds.