The generator matrix

 1  1  X  1  1  X
 0 X^3 X^3  0 X^3  0

generates a code of length 6 over Z2[X]/(X^4) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+28x^6+3x^8

The gray image is a linear code over GF(2) with n=48, k=5 and d=24.
As d=24 is an upper bound for linear (48,5,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 5.
This code was found by Heurico 1.16 in 1.05e-007 seconds.