The generator matrix

 1  0  1  1  1
 0  1  1 X^3+X^2 X^3+X+1
 0  0  X X^2+X 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+64x^3+354x^4+1216x^5+344x^6+64x^7+5x^8

The gray image is a linear code over GF(2) with n=40, k=11 and d=12.
As d=15 is an upper bound for linear (40,11,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 11.
This code was found by Heurico 1.16 in 0.031 seconds.