The generator matrix

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

generates a code of length 12 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+60x^12+3x^16

The gray image is a linear code over GF(2) with n=48, k=6 and d=24.
As d=24 is an upper bound for linear (48,6,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 6.
This code was found by Heurico 1.16 in 0.000302 seconds.