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

generates a code of length 34 over F8[X]/(X^2) who´s minimum homogenous weight is 224.

Homogenous weight enumerator: w(x)=1x^0+35x^224+245x^232+3584x^238+168x^240+35x^264+28x^272

The gray image is a linear code over GF(8) with n=272, k=4 and d=224.
This code was found by Heurico 1.16 in 0.00899 seconds.