The generator matrix
1 1 1 1 X 1
0 X 0 X^2+X X^2 0
0 0 X^2 X^2 X^2 0
generates a code of length 6 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+5x^4+10x^5+37x^6+4x^7+2x^8+2x^9+3x^10
The gray image is a linear code over GF(2) with n=24, k=6 and d=8.
This code was found by Heurico 1.16 in 0.000107 seconds.