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

generates a code of length 81 over GR(64,4) who´s minimum homogenous weight is 536.

Homogenous weight enumerator: w(x)=1x^0+154x^536+112x^540+112x^542+448x^543+1470x^544+1736x^545+2240x^548+3304x^550+4200x^551+6349x^552+5936x^553+4816x^556+8232x^558+9800x^559+11284x^560+12096x^561+5936x^564+23352x^566+23352x^567+23660x^568+22736x^569+10752x^572+22344x^574+19544x^575+17542x^576+14840x^577+4816x^580+280x^584+224x^592+168x^600+98x^608+98x^616+56x^624+28x^632+21x^640+7x^648

The gray image is a code over GF(8) with n=648, k=6 and d=536.
This code was found by Heurico 1.16 in 19.8 seconds.