The generator matrix

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

generates a code of length 6 over Z2[X]/(X^4) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+160x^3+1111x^4+6368x^5+17488x^6+6368x^7+1111x^8+160x^9+1x^12

The gray image is a linear code over GF(2) with n=48, k=15 and d=12.
This code was found by Heurico 1.16 in 0.281 seconds.