The generator matrix

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

generates a code of length 35 over F8[X]/(X^2) who´s minimum homogenous weight is 208.

Homogenous weight enumerator: w(x)=1x^0+546x^208+1862x^216+2835x^224+4060x^232+5019x^240+229376x^245+6412x^248+6384x^256+4004x^264+1407x^272+238x^280

The gray image is a linear code over GF(8) with n=280, k=6 and d=208.
This code was found by Heurico 1.16 in 19.7 seconds.