The generator matrix

 1  0  1  1  1  1
 0  1 X+1 X^2+X X^3+X^2 X^2+X
 0  0 X^3  0 X^3  0
 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+42x^4+176x^5+588x^6+176x^7+37x^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 1.05e-007 seconds.