The generator matrix
1 1 1 1 X X X
0 X^3 0 X^3 0 X^3 0
0 0 X^3 X^3 X^3 X^3 0
generates a code of length 7 over Z2[X]/(X^4) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+6x^6+48x^7+7x^8+2x^10
The gray image is a linear code over GF(2) with n=56, k=6 and d=24.
This code was found by Heurico 1.16 in -3.24e-008 seconds.