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

generates a code of length 64 over Z27 who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+96x^111+192x^114+230x^117+208x^120+162x^122+220x^123+972x^125+188x^126+15066x^128+180x^129+1296x^131+174x^132+180x^135+140x^138+132x^141+104x^144+64x^147+32x^150+26x^153+12x^156+6x^159+2x^183

The gray image is a code over GF(3) with n=576, k=9 and d=333.
This code was found by Heurico 1.16 in 3.32 seconds.