The generator matrix
1 1 1 1 X X X
0 X 0 X^3+X^2+X X^2+X X^2+X X^2+X
0 0 X^3+X^2 X^2 0 0 X^3
0 0 0 X^3 0 X^3 X^3
0 0 0 0 X^3 X^3 0
generates a code of length 7 over Z2[X]/(X^4) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+75x^4+64x^5+304x^6+1152x^7+319x^8+64x^9+64x^10+5x^12
The gray image is a linear code over GF(2) with n=56, k=11 and d=16.
This code was found by Heurico 1.16 in 3.62e-008 seconds.