The generator matrix

 1  0  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  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  1  1  1  3  1  1  1  1  1  1  1  1  1  1  1  1  1 3a  1  1  1  1  1
 0  1  1  a 7a+7 8a+4 3a+5 8a+5 8a a+5  0 a+5 8a 8a+5 8a+4  1  a 7a+7 3a+7 3a+5 a+5 8a+5 7a+7 8a+4  1  a 3a+7 2a+5 3a+7 8a+7 a+7  0 8a 2a+5 a+8  3 8a+3 5a+5 8a+7 a+8 3a a+3 3a+5 7a+8 6a+5 4a+8 a+3  6 2a+2  1 8a+3 6a+5  8 2a+2 5a+7 8a+3 3a a+3 a+7 a+7 6a+1 3a+3 8a+5  1 2a+2 a+8 4a  0  0
 0  0 3a+6  0 3a+6  3 6a+6 6a+6  6 3a 3a+6 3a  3 3a  3  3 6a+6  6 3a+6 3a+3 6a+6  6  0 3a  6  6  3 3a 6a 6a+3 6a 6a+3 6a+6 3a+3  6 6a+3 3a+6 3a+6  6 6a+3  0 3a 3a+6  6 6a 6a+3 6a 6a 3a+3  0  3 6a+3 3a+3 6a+6 3a+3 3a+3 3a 6a 6a+6 6a 3a+3 3a+3 6a  3 6a  0 3a+6 3a+3  0
 0  0  0  3 3a+6 3a+6  3 3a  3 3a+3 6a 6a+6 6a 6a+3  0 6a+6 3a+3 3a+6 3a 3a+3 6a 3a 6a+6  6  0 3a+3 3a  0 6a+6 3a+6  3 6a 6a+6 3a 6a  6  3 6a+3  0  3 6a+6 6a+6 3a+3  0  6 3a  0 6a+3 6a+6 3a  3  0 3a  6 6a  6  6  3 3a+3 3a 3a+3 6a+6 3a+3 3a 6a+3  6 6a+3 3a+3  0

generates a code of length 69 over GR(81,9) who´s minimum homogenous weight is 513.

Homogenous weight enumerator: w(x)=1x^0+56x^513+216x^517+696x^522+72x^523+144x^524+2304x^526+1440x^530+6712x^531+2160x^532+3168x^533+9576x^535+8640x^539+23240x^540+6696x^541+7776x^542+18792x^544+36720x^548+79792x^549+20664x^550+21024x^551+40032x^553+58176x^557+104000x^558+22896x^559+20376x^560+34056x^562+520x^567+576x^576+440x^585+256x^594+176x^603+40x^612+8x^621

The gray image is a code over GF(9) with n=621, k=6 and d=513.
This code was found by Heurico 1.16 in 40.3 seconds.