The generator matrix

 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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  3  1  1  1  1  1  3  1  3  3  1  1  1  1  1  1  1  3  3  1  1
 0  9  0  0  0  0  0  0  0  0  0  0  0  0 18  9 18  9 18  9  0  9  9 18  0  9 18  9 18 18  9 18  9 18  0 18  0  9 18 18  9  0  0  0  9  9 18  9 18  0  9  9  9  9  9 18  0  0 18  9  0  9  0  9  0
 0  0  9  0  0  0  0  0  0  0  0  9 18 18  0 18 18  9 18 18 18 18  0  9  9  9  0  9  0 18 18  9 18  0  9  9  0  9 18  0 18  9  9 18  0 18  9  9  0 18  0 18  9  9  0 18 18  9 18 18  0  0  9  9  0
 0  0  0  9  0  0  0  0  9 18 18 18  0  0  0 18 18  0 18  9 18  9 18 18 18  9 18 18  0  9 18 18 18  0  0  9  9  9  0  9 18 18  9  0 18  9  0  9  9 18  9 18 18  0  9  9 18 18  0  0  9 18 18  0  0
 0  0  0  0  9  0  0  9 18  0 18  0  0 18  0  0  9 18 18 18 18  9  9  9 18 18  0  9  0  9  0 18  0  9 18  0 18  9  9  0 18  0 18  9 18 18  0  0 18 18 18  9  9 18  0  0  0 18 18 18  0 18 18  0  0
 0  0  0  0  0  9  0 18 18  9  0 18 18 18 18 18  9  9  9  9 18  9 18  9  9 18 18  0  9  9  9  9  9  0 18  0  9  0  0  0 18  9  0  0 18 18  0 18  0  0  9  0  9  9  9  0  9 18  9  0  0  0  9  0  0
 0  0  0  0  0  0  9 18 18 18 18 18 18  9  9  0  0  0  0  9  9  0 18  0 18  9  0  0 18  0  0 18 18 18  9 18 18 18  9 18  0 18  9  9  9  9  0 18  0 18 18 18  9  9  9  0  9 18  9 18 18  0  0  9  9

generates a code of length 65 over Z27 who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+40x^111+110x^114+238x^117+6x^118+220x^120+72x^121+198x^123+360x^124+206x^126+960x^127+198x^129+14562x^130+178x^132+1152x^133+152x^135+384x^136+144x^138+142x^141+138x^144+90x^147+62x^150+44x^153+10x^156+6x^159+4x^162+4x^168+2x^177

The gray image is a code over GF(3) with n=585, k=9 and d=333.
This code was found by Heurico 1.16 in 3.33 seconds.