The generator matrix

 1  1  1  1  X  X
 0  X  0 X^2+X X^2+X X^3+X^2+X
 0  0 X^3+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+192x^5+500x^6+192x^7+65x^8+4x^10

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 6.87e-008 seconds.