The generator matrix

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

generates a code of length 43 over GR(64,4) who´s minimum homogenous weight is 288.

Homogenous weight enumerator: w(x)=1x^0+245x^288+1680x^289+784x^291+2352x^292+1232x^296+5600x^297+1120x^299+1568x^300+2499x^304+10640x^305+1680x^307+3248x^308+70x^312+21x^320+7x^328+14x^336+7x^344

The gray image is a code over GF(8) with n=344, k=5 and d=288.
This code was found by Heurico 1.16 in 0.135 seconds.