The generator matrix

 1  0  1  1  1
 0  1  0  0 X^2
 0  0  X  0  0
 0  0  0  X  0
 0  0  0  0  X

generates a code of length 5 over Z2[X]/(X^3) who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+14x^1+77x^2+232x^3+690x^4+2068x^5+690x^6+232x^7+77x^8+14x^9+1x^10

The gray image is a linear code over GF(2) with n=20, k=12 and d=2.
This code was found by Heurico 1.16 in 0.00245 seconds.