The generator matrix

 1  0  0  1  1  1  1
 0  1  0  1  a a^2 a^6*X+a^3
 0  0  1 a^6  a a^4  1

generates a code of length 7 over F8[X]/(X^2) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+1176x^35+147x^40+9408x^42+16464x^43+147x^48+111104x^49+65856x^50+57624x^51+217x^56

The gray image is a linear code over GF(8) with n=56, k=6 and d=35.
This code was found by Heurico 1.16 in 0.474 seconds.