The generator matrix

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

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+97x^4+338x^5+1181x^6+332x^7+94x^8+2x^9+3x^10

The gray image is a linear code over GF(2) with n=48, k=11 and d=16.
As d=19 is an upper bound for linear (48,11,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 11.
This code was found by Heurico 1.16 in 0.015 seconds.