The generator matrix
1 0 1 1 1 1
0 1 1 X^3+X^2 X^3+X+1 0
0 0 X X^2+X X^2 0
0 0 0 X^3 X^3 X^3
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+30x^3+146x^4+642x^5+2460x^6+642x^7+141x^8+30x^9+4x^10
The gray image is a linear code over GF(2) with n=48, k=12 and d=12.
This code was found by Heurico 1.16 in -3.24e-008 seconds.