The generator matrix
1 0 0 1 1 1 1
0 1 0 1 X^2+X X^2 0
0 0 1 1 X+1 X^2+X+1 0
0 0 0 X^3 0 X^3 X^3
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+78x^4+318x^5+1552x^6+4298x^7+1553x^8+306x^9+80x^10+6x^11
The gray image is a linear code over GF(2) with n=56, k=13 and d=16.
This code was found by Heurico 1.16 in 0.031 seconds.