The generator matrix

 1  1  1  X  X  X
 0 X^3  0  0 X^3 X^3
 0  0 X^3 X^3 X^3  0

generates a code of length 6 over Z2[X]/(X^4) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+6x^5+52x^6+3x^8+2x^9

The gray image is a linear code over GF(2) with n=48, k=6 and d=20.
This code was found by Heurico 1.16 in 3.62e-008 seconds.