The generator matrix
1 1 X X 1 1
0 X X 0 0 0
0 0 X^2 X^3+X^2 0 0
0 0 0 X^3 0 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+24x^2+16x^3+103x^4+304x^5+1152x^6+304x^7+103x^8+16x^9+24x^10+1x^12
The gray image is a linear code over GF(2) with n=48, k=11 and d=8.
This code was found by Heurico 1.16 in 3.81e-009 seconds.