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

generates a code of length 40 over GR(64,4) who´s minimum homogenous weight is 269.

Homogenous weight enumerator: w(x)=1x^0+3360x^269+2520x^270+189x^272+6720x^277+3024x^278+224x^280+11424x^285+5208x^286+63x^288+7x^304+28x^320

The gray image is a code over GF(8) with n=320, k=5 and d=269.
This code was found by Heurico 1.16 in 15.6 seconds.