The generator matrix

 1  0  0  1  1
 0  1  0  1  0
 0  0  1  1  0
 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+89x^2+504x^3+2278x^4+10640x^5+2278x^6+504x^7+89x^8+1x^10

The gray image is a linear code over GF(2) with n=40, k=14 and d=8.
This code was found by Heurico 1.16 in 0.063 seconds.