The generator matrix

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

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+29x^4+226x^5+517x^6+220x^7+26x^8+2x^9+3x^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 0.031 seconds.