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.