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

generates a code of length 42 over GR(81,9) who´s minimum homogenous weight is 306.

Homogenous weight enumerator: w(x)=1x^0+320x^306+360x^307+216x^312+288x^313+720x^314+2504x^315+4032x^316+1296x^320+5184x^321+3024x^322+4320x^323+6720x^324+12960x^325+20736x^329+41472x^330+16416x^331+18360x^332+20696x^333+42192x^334+82944x^338+110592x^339+32760x^340+29088x^341+26800x^342+45432x^343+896x^351+704x^360+336x^369+72x^378

The gray image is a code over GF(9) with n=378, k=6 and d=306.
This code was found by Heurico 1.16 in 23.3 seconds.