The generator matrix

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

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+70x^4+448x^5+1012x^6+448x^7+65x^8+4x^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 -6.48e-008 seconds.