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

generates a code of length 35 over F8[X]/(X^2) who´s minimum homogenous weight is 224.

Homogenous weight enumerator: w(x)=1x^0+595x^224+448x^231+770x^232+6272x^239+770x^240+21952x^247+623x^248+518x^256+448x^264+308x^272+63x^280

The gray image is a linear code over GF(8) with n=280, k=5 and d=224.
This code was found by Heurico 1.16 in 78 seconds.