The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  X  1  1  1  1  1  1  X  1  1  1  1  1
 0  1  1  a a^6*X+a^2 a^3 a^6*X+a^4 a^5 a^6*X+a^6  0 a^6*X+1  a a^6*X+a^2 a^6*X+a^4 a^6*X+a^6 a^3 a^5  1  X a^5*X+a^6 X+a X+a^5  1 a^6*X+1 a^5*X+a^2 X+a^3 a^5*X+a^4  X a^5*X+1  1 a^5*X X+a X+a^5 a^5*X+1 a*X
 0  0 a^6*X a*X  X  0 a^3*X a^5*X a^4*X a^2*X a*X a^4*X a^3*X  X a^6*X a^5*X a^2*X a*X a^6*X a*X a^5*X  0 a^6*X a^3*X a^4*X  X a^2*X a^5*X a^2*X a^4*X a*X  X a^3*X  X a^2*X

generates a code of length 35 over F8[X]/(X^2) who´s minimum homogenous weight is 232.

Homogenous weight enumerator: w(x)=1x^0+742x^232+1008x^233+560x^234+784x^235+4263x^240+3360x^241+1120x^242+1120x^243+9751x^248+6384x^249+1904x^250+1680x^251+49x^256+7x^272+35x^280

The gray image is a linear code over GF(8) with n=280, k=5 and d=232.
This code was found by Heurico 1.16 in 0.118 seconds.