The generator matrix

 1  0  0  1 X^2 X^3+X
 0  1  0  X  1  1
 0  0  1  1  X X^2+X

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

Homogenous weight enumerator: w(x)=1x^0+201x^4+690x^5+2317x^6+684x^7+198x^8+2x^9+3x^10

The gray image is a linear code over GF(2) with n=48, k=12 and d=16.
As d=18 is an upper bound for linear (48,12,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 12.
This code was found by Heurico 1.16 in 0.031 seconds.