The generator matrix

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

generates a code of length 5 over Z2[X]/(X^4) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+8x^3+34x^4+176x^5+24x^6+8x^7+5x^8

The gray image is a linear code over GF(2) with n=40, k=8 and d=12.
This code was found by Heurico 1.16 in -3.24e-008 seconds.