The generator matrix
1 1 1 1 1 1 1
0 X 0 X a*X a*X a^5*X
0 0 X a^6*X a^2*X a^4*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+147x^48+3584x^49+217x^56
The gray image is a linear code over GF(8) with n=56, k=4 and d=40.
This code was found by Heurico 1.16 in 0.000569 seconds.