The generator matrix
1 1 X 1 1 1
0 X X 0 0 0
0 0 X^2 0 X^2 0
0 0 0 X^3+X^2 X^2 0
0 0 0 0 X^3 0
generates a code of length 6 over Z2[X]/(X^4) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+36x^2+48x^3+135x^4+720x^5+2216x^6+720x^7+135x^8+48x^9+36x^10+1x^12
The gray image is a linear code over GF(2) with n=48, k=12 and d=8.
This code was found by Heurico 1.16 in 3.81e-009 seconds.