The generator matrix

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

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+128x^3+738x^4+2368x^5+728x^6+128x^7+5x^8

The gray image is a linear code over GF(2) with n=40, k=12 and d=12.
As d=14 is an upper bound for linear (40,12,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 12.
This code was found by Heurico 1.16 in 0.015 seconds.