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

generates a code of length 86 over GR(64,4) who´s minimum homogenous weight is 574.

Homogenous weight enumerator: w(x)=1x^0+168x^574+504x^576+56x^577+168x^578+952x^579+2240x^580+1120x^581+1288x^582+889x^584+1680x^585+2240x^586+5152x^587+9744x^588+3976x^589+4760x^590+714x^592+4032x^593+4816x^594+11088x^595+17808x^596+5992x^597+5880x^598+476x^600+11760x^601+11648x^602+23072x^603+33712x^604+11032x^605+10976x^606+343x^608+11144x^609+9800x^610+17080x^611+22512x^612+6552x^613+5600x^614+322x^616+245x^624+203x^632+119x^640+119x^648+70x^656+63x^664+21x^672+7x^688

The gray image is a code over GF(8) with n=688, k=6 and d=574.
This code was found by Heurico 1.16 in 41.8 seconds.