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  2  2 2a^2+3  a a^2+3a+3 2a^2 3a^2+2 2a^2+3a+1 a^2+3a 3a^2+2a+3  a 3a^2+2 2a^2+3 3a^2+2a+3  1 2a^2+3a+1 a^2+3a a^2+3a+3 2a^2+2a+3 a+2 a^2+a 3a^2+2a+2 2a^2+3a+3 a^2+3a+1 3a^2+3 2a^2+2a+3 a+2 a^2+3a+1 a^2+a 3a 2a
 0  0  2 2a^2+2 2a^2+2a+2 2a 2a+2 2a^2 2a^2+2a  0 2a^2+2 2a 2a  2 2a^2 2a+2 2a^2+2a+2  2 2a^2+2a 2a^2 2a+2 2a^2+2 2a^2+2a+2  2 2a^2+2a  0 2a^2+2a+2 2a+2  0 2a^2 2a 2a^2+2a 2a^2+2  0

generates a code of length 34 over GR(64,4) 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 code over GF(8) with n=272, k=5 and d=224.
This code was found by Heurico 1.16 in 0.117 seconds.