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  1  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  X  X a^6*X+1  a a^5 a^2*X a^6*X+a^2 a^3 a^6*X+a^4 a^6*X+a^6  a a^6*X+a^2 a^6*X+1 a^6*X+a^6  1 a^3 a^6*X+a^4 a^5 a^5*X+1 X+a a^5*X+a^4 a^5*X+a^2 X+a^3 X+a^5 a^5*X+a^6 a^5*X+1 X+a X+a^5 a^5*X+a^4 a*X+a a*X
 0  0  X a^6*X a^5*X a*X a^3*X a^2*X a^4*X  0 a^6*X a*X a*X  X a^2*X a^3*X a^5*X  X a^4*X a^2*X a^3*X a^6*X a^5*X  X a^4*X  0 a^5*X a^3*X  0 a^2*X a*X a^4*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+105x^224+504x^225+1008x^226+560x^227+784x^228+1036x^232+3024x^233+3360x^234+1120x^235+1120x^236+2828x^240+7224x^241+6384x^242+1904x^243+1680x^244+70x^248+14x^256+14x^264+28x^272

The gray image is a linear code over GF(8) with n=272, k=5 and d=224.
This code was found by Heurico 1.16 in 0.117 seconds.