The generator matrix

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

generates a code of length 34 over F8[X]/(X^2) who´s minimum homogenous weight is 220.

Homogenous weight enumerator: w(x)=1x^0+1344x^220+721x^224+1176x^225+3360x^226+14112x^227+8904x^228+1344x^231+8806x^232+7056x^233+11200x^234+30016x^235+18480x^236+3584x^238+9408x^239+30254x^240+16856x^241+21280x^242+49056x^243+25032x^244+49x^248+77x^256+21x^264+7x^272

The gray image is a linear code over GF(8) with n=272, k=6 and d=220.
This code was found by Heurico 1.16 in 6.41 seconds.