The generator matrix
1 0 1 1 1 1 1
0 1 1 a a^6*X+a^2 a^3 a^6*X+a^4
0 0 a^6*X a*X a^3*X a^5*X X
generates a code of length 7 over F8[X]/(X^2) who´s minimum homogenous weight is 40.
Homogenous weight enumerator: w(x)=1x^0+147x^40+3136x^42+147x^48+7168x^49+21952x^50+217x^56
The gray image is a linear code over GF(8) with n=56, k=5 and d=40.
This code was found by Heurico 1.16 in 0.00787 seconds.