The generator matrix

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

generates a code of length 56 over GR(81,9) who´s minimum homogenous weight is 414.

Homogenous weight enumerator: w(x)=1x^0+192x^414+360x^419+216x^420+968x^423+72x^424+288x^425+2160x^426+2880x^427+3888x^428+2952x^429+1120x^432+1728x^433+3024x^434+12960x^435+10800x^436+13392x^437+7992x^438+1040x^441+13824x^442+16416x^443+55080x^444+39744x^445+41760x^446+20952x^447+904x^450+36864x^451+32760x^452+87264x^453+51552x^454+45576x^455+20376x^456+720x^459+680x^468+440x^477+352x^486+128x^495+16x^504

The gray image is a code over GF(9) with n=504, k=6 and d=414.
This code was found by Heurico 1.16 in 32.9 seconds.