The generator matrix

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

generates a code of length 68 over GR(64,4) who´s minimum homogenous weight is 448.

Homogenous weight enumerator: w(x)=1x^0+210x^448+56x^450+168x^452+3808x^455+1043x^456+560x^457+2968x^458+2296x^460+10696x^463+2807x^464+2800x^465+10920x^466+4648x^468+18984x^471+10269x^472+10640x^473+33544x^474+11816x^476+32984x^479+17185x^480+14672x^481+38528x^482+9744x^484+19544x^487+357x^488+266x^496+231x^504+161x^512+168x^520+35x^528+28x^536+7x^544

The gray image is a code over GF(8) with n=544, k=6 and d=448.
This code was found by Heurico 1.16 in 16.4 seconds.