The generator matrix

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

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+87x^4+384x^5+1104x^6+384x^7+87x^8+1x^12

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 6.87e-008 seconds.