The generator matrix

 1  1  1  1 X^3  0
 0  X  0  X  X  X
 0  0  X  X X^2 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+74x^4+168x^5+552x^6+144x^7+77x^8+8x^9

The gray image is a linear code over GF(2) with n=48, k=10 and d=16.
This code was found by Heurico 1.16 in -3.24e-008 seconds.